Journal of Logic and Computation - Advance Access

A Relevance-theoretic Framework for Constructing and Deconstructing Enthymemes

Black, E., Hunter, A. — Thu, 12 Nov 2009 03:24:44 PST

In most proposals for logic-based models of argumentation dialogues between agents, the arguments exchanged are logical arguments of the form <,> where is a set of formulae (called the support) and is a formula (called the claim) such that is consistent and entails . However, arguments presented by real-world agents do not normally fit the mould of being logical arguments. They are normally enthymemes, and so they only explicitly represent some of the premises for entailing their claim and/or they do not explicitly state their claim. For example, for a claim that ‘you need an umbrella today’, a husband may give his wife the premise ‘the weather report predicts rain’. Clearly, the premise does not entail the claim, but it is easy for the wife to identify the assumed knowledge used by the husband in order to reconstruct the intended argument correctly (i.e. ‘if the weather report predicts rain, then you need an umbrella’). Whilst humans are constantly handling examples like this, proposals for logic-based formalizations of the process remain underdeveloped. In this article, we present a logic-based framework for handling enthymemes, some design features of which are influenced by aspects of relevance theory (proposed by Sperber and Wilson). In particular, we use the ideas of maximizing cognitive effect and minimizing cognitive effort in order to enable a proponent of an intended logical argument to construct an enthymeme appropriate for the intended recipient, and for the intended recipient to deconstruct the intended logical argument from the enthymeme. We relate our framework back to Sperber andWilson's relevance theory via some formal properties.

Book Review * Relation Algebras by Games, by Robin Hirsch and Ian Hodkinson

Kikot, S. — Tue, 10 Nov 2009 04:28:41 PST

The Complexity of the Warranted Formula Problem in Propositional Argumentation

Hirsch, R., Gorogiannis, N. — Tue, 10 Nov 2009 04:28:40 PST

The notion of warrant or justification is one of the central concepts in formal models of argumentation. The dialectical definition of warrant is expressed in terms of recursive defeat: an argument is warranted if each of its counter-arguments is itself defeated by a warranted counter-argument. However, few complexity results exist on checking whether an argument is warranted in the context of deductive models of argumentation, i.e. models where an argument is a deduction of a claim from a set of premises using some logic. We investigate the computational complexity of checking whether a claim is warranted in propositional argumentation under two natural definitions of warrant and show that it is PSPACE-complete in both cases.

Paraconsistent Machines and their Relation to Quantum Computing

Agudelo, J. C., Carnielli, W. — Tue, 10 Nov 2009 04:28:39 PST

We describe a method to axiomatize computations in deterministic Turing machines (TMs). When applied to computations in non-deterministic TMs, this method may produce contradictory (and therefore trivial) theories, considering classical logic as the underlying logic. By substituting in such theories the underlying logic by a paraconsistent logic we define a new computation model, the paraconsistent Turing machine. This model allows a partial simulation of superposed states of quantum computing. Such a feature allows the definition of paraconsistent algorithms which solve (with some restrictions) the well-known Deutsch's and Deutsch-Jozsa problems. This first model of computation, however, does not adequately represent the notions of entangled states and relative phase, which are key features in quantum computing. In this way, a more sharpened model of paraconsistent TMs is defined, which better approaches quantum computing features. Finally, we define complexity classes for such models, and establish some relationships with classical complexity classes.

Causal Relevance and Relevant Causation

Jacquette, D. — Tue, 10 Nov 2009 04:28:39 PST

The interconnectedness of all events in the causal matrix suggests that the so-called informal fallacy of post hoc, ergo propter hoc reasoning is not deductively invalid. It may be preferable then to consider post hoc, propter hoc as violating a pragmatic concept of causal relevance. A leading pragmatic account of relevance defines it as the caused closure of a cognitive agenda, to which it seems necessary to add that such closure be relevantly caused, and not by such contingencies as the inquirer's death or incapacity, magic philosopher's pills or the like. This in turn involves the concept of relevant causation in a vicious circularity. The implication may then be that relevant causation, like time and space as pure forms of intuition in Kant's Transcendental Aesthetic, cannot be defined or reductively characterized in terms of more primitive concepts, let alone derived empirically or pragmatically from the contents of experience or purpose of an action. Causation and causal relevance on this proposal constitute instead part of the mind's innate quasi-metaphysical bedrock of scientific explanation.

Argument Relevance as the Right Kind of Epistemic Reason

Adler, J. E. — Tue, 10 Nov 2009 04:28:38 PST

A defense of the view that there is a central purpose in presenting an argument: to establish its conclusion, and so to secure belief in it. Relevance is then relevance to that purpose. To deem a statement relevant to an argument is to claim that it functions as a kind of epistemic reason pertaining to the cogency of an argument to establish its conclusion. Criticism of Walton's dialogue-relative understanding of relevance, as well as the probabilistic criterion of relevance or evidence.

Answer Set Programming with Resources

Costantini, S., Formisano, A. — Fri, 06 Nov 2009 01:41:03 PST

In this article, we propose an extension of Answer Set Programming (ASP) to support declarative reasoning on consumption and production of resources. We call the proposed extension RASP, standing for ‘Resourced ASP’. Resources are modeled by introducing special atoms, called amount-atoms, to which we associate quantities that represent the available amount of a certain resource. The ‘firing’of aRASP rule involving amount-atoms can both consume and produce resources. A RASP rule can be fired several times, according to its definition and to the available quantities of required resources. We define the semantics for RASP programs by extending the usual answer set semantics. Different answer sets correspond to different possible allocations of available resources. We then propose an implementation based on standard ASP-solvers. The implementation consists of a standard translation of each RASP rule into a set of plain ASP-rules and of an inference engine that manages the firing of RASP rules.

Relevance in Cooperation and Conflict

Franke, M., De Jager, T., Van Rooij, R. — Fri, 06 Nov 2009 01:41:03 PST

Linguistic pragmatics assumes that conversation is a by-and-large cooperative endeavour. Although clearly reasonable and helpful, this is an idealization and it pays to ask what happens to natural language interpretation if the presumption of cooperativity is dropped, be that entirely or only to some degree. Game theory suggests itself as a formal tool for modelling the different degrees in which speaker and hearer may or may not have common interests, and it is in this game-theoretic light that this article investigates in particular a notion of speaker-relevance and its impact on the question why we communicate cooperatively in most cases and what happens to pragmatic phenomena such as conversational implicatures if full cooperation cannot be assumed.

Relevance Realization and the Emerging Framework in Cognitive Science

Vervaeke, J., Lillicrap, T. P., Richards, B. A. — Mon, 26 Oct 2009 22:47:11 PDT

We argue that an explanation of relevance realization is a pervasive problem within cognitive science, and that it is becoming the criterion of the cognitive in terms of which a new framework for doing cognitive science is emerging. We articulate that framework and then make use of it to provide the beginnings of a theory of relevance realization that incorporates many existing insights implicit within the contributing disciplines of cognitive science. We also introduce some theoretical and potentially technical innovations motivated by the articulation of those insights. Finally, we show how the explication of the framework and development of the theory help to clear up some important incompleteness and confusions within both Montague's work and Sperber and Wilson's theory of relevance.

Relevance and Conjunction

Mares, E. D. — Tue, 20 Oct 2009 23:32:12 PDT

This article gives an interpretation and justification of extensional and intensional conjunction in the relevant logic R. The interpretive frameworks are Anderson and Belnap's natural deduction system and the theory of situated inference from Mares, Relevant Logic.

On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice

Bou, F., Esteva, F., Godo, L., Rodriguez, R. O. — Wed, 07 Oct 2009 23:34:11 PDT

This article deals with many-valued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated in the residuated lattice (and so defining the minimum modal logic), the ones evaluated in the idempotent elements and the ones only evaluated in 0 and 1. We show how to expand an axiomatization, with canonical truth-constants in the language, of a finite residuated lattice into one of the modal logic, for each one of the three basic classes of Kripke frames. We also provide axiomatizations for the case of a finite MV chain but this time without canonical truth-constants in the language.

A Simple Proof of Completeness and Cut-admissibility for Propositional Godel Logic

Avron, A. — Wed, 23 Sep 2009 23:41:13 PDT

We provide a constructive, direct and simple proof of the completeness of the cut-free part of the hypersequential calculus HG for Gödel logic (thereby proving both completeness of the calculus for its standard semantics, and the admissibility of the cut rule in the full calculus). We then extend the results and proofs to derivations from assumptions, showing that such derivations can be confined to those in which cuts are made only on formulas which occur in the assumptions. The article is self-contained, and no previous knowledge concerning HG (or even Gödel logic) is needed for understanding it.

A Notion of Coherence for Books on Conditional Events in Many-valued Logic

Montagna, F. — Thu, 17 Sep 2009 00:14:08 PDT

We introduce a new approach to conditional probability over many-valued events, which is based on bets. Then we show that this approach fits with Kroupa's approach, and we give two characterizations of coherence for books on conditional many-valued events, the first one based on states, and the second one based on logical coherence of a suitable theory on many-valued logic.

On the Structure of Finite Integral Commutative Residuated Chains

Horcik, R. — Thu, 17 Sep 2009 00:14:07 PDT

Among the class of finite integral commutative residuated chains (ICRCs), we identify those algebras which can be obtained as a nuclear retraction of a conuclear contraction of a totally ordered Abelian -group. We call the ICRCs satisfying this condition regular. Then we discuss the structure of finite regular ICRCs. Finally, we prove that the class of regular members generate a strictly smaller variety than the variety generated by ICRCs.

Computing Minimal Axiomatizations in Godel Propositional Logic

Aguzzoli, S., D'Antona, O. M., Marra, V. — Thu, 17 Sep 2009 00:14:06 PDT

We solve the minimization problem for finitely axiomatizable theories in Gödel infinite-valued propositional logic. That is, we obtain an algorithm that when input a formula (X₁,...,X_n) outputs a formula β(X₁,...,X_m) such that (i) the theories singly axiomatized by {} and {β} have isomorphic algebraic semantics, and (ii) if β'(X₁,...,X_m_') is any formula satisfying (i), then m'≥m.

A Proof System for Abstract Non-interference

Giacobazzi, R., Mastroeni, I. — Thu, 17 Sep 2009 00:14:05 PDT

In this article, we provide an inductive proof system for a notion of abstract non-interference (ANI) which fits in every field of computer science where we are interested in observing how different programs data interfere with each other. The idea is to abstract from language-based security and consider generically data as distinguished between internal (that has to be protected by the program) and observable. In this more general context, we derive a proof system that allows us -to characterize ANI properties inductively on the syntactic structure of programs. We finally show how this framework can be instantiated to language-based security.

Arithmetical Complexity of First-order Predicate Fuzzy Logics Over Distinguished Semantics

Montagna, F., Noguera, C. — Thu, 17 Sep 2009 00:52:27 PDT

All promiment examples of first-order predicate fuzzy logics are undecidable. This leads to the problem of the arithmetical complexity of their sets of tautologies and satisfiable sentences. This article is a contribution to the general study of this problem. We propose the classes of first-order core and -core fuzzy logics as a good framework to address these arithmetical complexity issues. We obtain general results providing lower bounds for the complexities associated with arbitrary semantics, and we compute upper bounds and exact positions in the arithmetical hierarchy for distinguished semantics: general semantics given by all chains, finite-chain semantics, standard semantics and rational semantics.

Codd's Relational Model from the Point of View of Fuzzy Logic

Belohlavek, R., Vychodil, V. — Mon, 14 Sep 2009 22:21:33 PDT

The article deals with Codd's relational model of data and its fuzzy logic extensions. Our main purpose is to examine, from the point of view of fuzzy logic in the narrow sense, some of the extensions proposed in the literature and the relationships between them. We argue that fuzzy logic in the narrow sense is important for the fuzzy logic extensions because it provides conceptual and methodological foundations, clarity and simplicity. We present several comparative observations as well as new technical results.

Structural Description of a Class of Involutive Uninorms via Skew Symmetrization

Jenei, S. — Sun, 13 Sep 2009 03:26:59 PDT

The main ‘philosophical’ outcome of this article is to demonstrate that the structural description of residuated lattices requires the use of the co-residuated setting. A construction, called skew symmetrization, which generalizes the well-known representation of an ordered Abelian group obtained from the positive (or negative) cone of the algebra is introduced here. Its definition requires leaving the accustomed residuated setting and entering the co-residuated setting. It is shown that every uninorm on [0, 1] with an involution defined by the residual complement with respect to the unit and having the unit as the fixed point of the involution can be described as the skew symmetrization of its underlying t-norm or underlying t-conorm.

Comments on Interpretability and Decidability in Fuzzy Logic

Hajek, P. — Sun, 13 Sep 2009 03:26:59 PDT

A particular notion of an interpretation of a theory over a fuzzy predicate logic in another such theory is discussed. For interpretability with the domain defined by a provably crisp formula, which is of course a syntactical notion, a semantic characterization is established. In the last section, we discuss the question of whether the extension of a decidable theory by a single new axiom is decidable and present an erratum to the paper (Hájek, 2007, Fundamenta informaticae, 81, 155–163).

A Nominal Axiomatization of the Lambda Calculus

Gabbay, M. J., Mathijssen, A. — Sun, 13 Sep 2009 03:26:58 PDT

The lambda calculus is fundamental in computer science. It resists an algebraic treatment because of capture-avoidance sideconditions. Nominal algebra is a logic of equality designed for specifications involving binding. We axiomatize the lambda calculus using nominal algebra, demonstrate how proofs with these axioms reflect the informal arguments on syntax and we prove the axioms to be sound and complete. We consider both non-extensional and extensional versions (alpha-beta and alpha-beta-eta equivalence). This connects the nominal approach to names and binding with the view of variables as a syntactic convenience for describing functions. The axiomatization is finite, close to informal practice and it fits into a context of other research such as nominal rewriting and nominal sets.

On White's Expansion of Lukasiewicz Logic

Hajek, P. — Fri, 11 Sep 2009 07:52:53 PDT

Avariant of Lukasiewicz logic defined in a remark in White's 1979 paper on the consistency of the axiom of comprehension in the infinite-valued predicate logic of Lukasiewicz is studied; it is shown that the logic in question is an interesting expansion of Lukasiewicz logic which deserves further investigation together with its further expansions. Several formulas are proved in it and some model theory is offered. In the Appendix A, it is shown that a set theory with full comprehension over this logic (claimed consistent by White) is contradictory.

A Remark on Superintuitionistic Predicate Logics of Kripke Frames with Constant and with Nested Domains

Skvortsov, D. — Fri, 11 Sep 2009 07:52:52 PDT

The superintuitionistic predicate logics (without or with equality) of all predicate Kripke frames with nested domains over a fixed poset W (a set of possible worlds) are embeddable in the logic (without equality) of all Kripke frames with constant domains over W. Therefore, Takano's result [13] on finite axiomatizability of the logic of Kripke frames with constant domains over the set of real numbers implies the recursive axiomatizability of the corresponding logics with nested domains. Other consequences are mentioned as well.

Intuitionistic Dual-intuitionistic Nets

Laurent, O. — Tue, 25 Aug 2009 23:33:22 PDT

The intuitionistic sequent calculus (at most one formula on the right-hand side of sequents) comes with a natural dual system: the dual-intuitionistic sequent calculus (at most one formula on the left-hand side). We explain how the duality between these two systems exactly corresponds to the intensively studied duality between call-by-value systems and call-by-name systems for classical logic. Relying on the uniqueness of the computational behaviour underlying these four logics (intuitionistic, dual-intuitionistic, call-by-value classical and call-by-name classical), we define a generic syntax of nets which can be used for any of these logics.

Eskolemization in Intuitionistic Logic

Baaz, M., Iemhoff, R. — Tue, 25 Aug 2009 23:33:21 PDT

In Baaz and Iemhoff (2006, Annals of Pure and Applied Logic, 142, 269–295), an alternative skolemization method called eskolemization was introduced that is sound and complete for existence logic with respect to existential quantifiers. Existence logic is a conservative extension of intuitionistic logic by an existence predicate. Therefore, eskolemization provides a skolemization method for intuitionistic logic as well. All proofs in Baaz and Iemhoff (2006, Annals of Pure and Applied Logic, 142, 269–295) were semantical. In this article, a proof-theoretic proof of the completeness of eskolemization with respect to existential quantifiers is presented.

On two Attempts of Describing Propositional Realizability Logic

Plisko, V. — Mon, 17 Aug 2009 06:38:42 PDT

The study of propositional realizability logic was initiated in the 50th of the last century. Unfortunately, no description of the class of realizable propositional formulas is found up to now. Nevertheless, some attempts of such a description were made. In 1974, the author proved that every known realizable propositional formula has the property that every one of its closed arithmetical instances is deducible in the system obtained by adding Extended Church's Thesis and Markov Principle as axiom schemes to Intuitionistic Arithmetic. Visser calls this system Markov's Arithmetic. In 1990, another attempt of describing the class of realizable propositional formulas was made by Varpakhovskii who proposed a calculus in an extended propositional language and proved that all known realizable propositional formulas are deducible in this calculus. In this article we prove that every propositional formula deducible in Varpakhovskii's calculus has the property that each of its closed arithmetical instances is deducible in Markov's Arithmetic.

Arithmetical Completeness of the Intuitionistic Logic of Proofs

Dashkov, E. — Mon, 17 Aug 2009 06:38:41 PDT

Classical logic of proofs LP naturally extends propositional calculus to the language enriched with formulas meaning t is a proof of formula F. Intuitionistic logic of proofs iLP introduced by Artemov and Iemhoff was conjectured to be complete with respect to intuitionistic arithmetic HA. The article presents a proof of this conjecture.

Can we make the Second Incompleteness Theorem Coordinate Free?

Visser, A. — Wed, 12 Aug 2009 05:23:44 PDT

Is it possible to give a coordinate-free formulation of the Second Incompleteness Theorem? We pursue one possible approach to this question. We show that (i) cutfree consistency for finitely axiomatized theories can be uniquely characterized modulo EA-provable equivalence and (ii) consistency for finitely axiomatized sequential theories can be uniquely characterized modulo EA-provable equivalence. The case of infinitely axiomatized RE theories is more delicate. We carefully discuss this in the article.

A Topological Study of the Closed Fragment of GLP

Icard, T. — Wed, 12 Aug 2009 05:23:43 PDT

In this article, we study the canonical model for the closed fragment of GLP and establish its precise relationship with a universal model constructed by Ignatiev. In particular, we effectively characterize the canonical model in terms of a coordinate system based on sequences of ordinals up to ₀.We then define a simple topological model of this logic by defining a natural polytopology on the ordinal ₀ itself.

From Deep Inference to Proof Nets via Cut Elimination

Strassburger, L. — Mon, 10 Aug 2009 06:10:27 PDT

This article shows how derivations in the deep inference system SKS for classical propositional logic can be translated into proof nets. Since an SKS derivation contains more information about a proof than the corresponding proof net, we observe a loss of information which can be understood as ‘eliminating bureaucracy’. Technically, this is achieved by cut reduction on proof nets. As an intermediate step between the two extremes, SKS derivations and proof nets, we will see proof graphs representing derivations in ‘Formalism A’.

Verification of Games in the Game Description Language

Ruan, J., Van Der Hoek, W., Wooldridge, M. — Wed, 05 Aug 2009 06:02:37 PDT

The Game Description Language (GDL) is a special purpose declarative language for defining games. GDL is used in the AAAI General Game Playing Competition, which tests the ability of computer programs to play games in general, rather than just the ability to play a specific game. Participants in the competition are provided with a previously unknown game specified in GDL, and are required to dynamically and autonomously determine how best to play this game. Recently, there has been much interest in the use of strategic cooperation logics for reasoning about game-like scenarios—the Alternating-time Temporal Logic (ATL) of Alur, Henzinger, and Kupferman is perhaps the best known example. Such logics are specifically intended to support reasoning about game-theoretic properties of multi-agent systems. In short, the aim of this article is to make a concrete link between ATL and GDL, with the ultimate goal of using ATL to reason about GDL-specified games. We make the following contributions. First, we demonstrate that GDL can be understood as a specification language for ATL models, and prove that the problem of interpreting ATL formulae over propositional GDL descriptions is EXPTIME-complete. Second, we use ATL to characterize a class of ‘fair playability’ conditions, which might or might not hold of various games.

Max-based Prioritized Information Fusion without Commensurability

Benferhat, S., Lagrue, S., Rossit, J. — Wed, 22 Jul 2009 06:15:24 PDT

In the last decade, several approaches have been proposed for merging multiple and potentially conflicting pieces of information. Egalitarian fusion modes pick solutions that minimize the local dissatisfaction of each source (agent, expert), which is involved in the fusion process. When pieces of information to merge are prioritized, or ranked, most existing approaches assume that these priority degrees are commensurable, namely sources are assumed to share the same meaning of uncertainty scales. This article provides useful strategies for an egalitarian fusion of incommensurable ranked belief bases under constraints. In particular, it focuses on Max-based merging operators, and proposes a merging operator that allows to aggregate a set of ranked belief bases E. This operator is based on the concept of compatible scales. We provide three equivalent characterizations of this operator. The first one shows that Max-based merging of incommensurable belief bases can also be defined in terms of a Pareto-like ordering on possible worlds, denominated SMP ordering. The second one is based on the notion of compatible rankings defined on finite scales. The third one is only based on total pre-orders induced by ranked bases to merge. The last part of the article analyses rational postulates satisfied by our merging operator and compare it with some related works.

The Effects of Bounding Syntactic Resources on Presburger LTL

Demri, S., Gascon, R. — Wed, 22 Jul 2009 06:15:23 PDT

LTL over Presburger constraints is the extension of LTL where the atomic formulae are quantifier-free Presburger formulae having as free variables the counters at different states of the model. This logic is known to admit undecidable satisfiability and model-checking problems. We study decidability and complexity issues for fragments of LTL with Presburger constraints obtained by restricting the syntactic resources of the formulae (the number of variables, the maximal distance between two states for which counters can be compared and, to a smaller extent, the set of Presburger constraints), while preserving the strength of the logical operators. We provide a complete picture refining known results from the literature. We show that model-checking and satisfiability problems for the fragments of LTL with difference constraints restricted to two variables and distance one and to one variable and distance two are highly undecidable, enlarging significantly the class of known undecidable fragments. On the positive side, we prove that the fragment restricted to one variable and to distance one augmented with propositional variables is pspace-complete. Since the atomic formulae can state quantitative properties on the counters, this extends some results about model-checking pushdown systems and one-counter automata. In order to establish the pspace upper bound, we show that the non-emptiness problem for Büchi one-counter automata taking values in Z and allowing zero tests and sign tests, is only nlogspace-complete. Finally, we establish that model-checking one-counter automata with complete quantifier-free Presburger LTL restricted to one variable is also pspace-complete, whereas the satisfiability problem is undecidable.

A Logical and Computational Theory of Located Resource

Collinson, M., Monahan, B., Pym, D. — Wed, 22 Jul 2009 06:15:23 PDT

Experience of practical systems modelling suggests that the key conceptual components of a model of a system are processes, resources, locations and environment. In recent work, we have given a process-theoretic account of this view in which resources as well as processes are first-class citizens. This process calculus, SCRP, captures the structural aspects of the semantics of the Demos2k (D2K) modelling tool. D2K represents environment stochastically using a wide range of probability distributions and queue-like data structures. Associated with SCRP is a (bunched) modal logic, MBI, which combines the usual additive connectives of Hennessy–Milner logic with their multiplicative counterparts. In this article, we complete our conceptual framework by adding to SCRP and MBI an account of a notion of location that is simple, yet sufficiently expressive to capture naturally a wide range of forms of location, both spatial and logical. We also provide a description of an extension of the D2K tool to incorporate this notion of location.

Labelled Tableaux for Distributed Temporal Logic

Basin, D., Caleiro, C., Ramos, J., Vigano, L. — Tue, 07 Jul 2009 00:51:29 PDT

The distributed temporal logic DTL is a logic for reasoning about temporal properties of discrete distributed systems from the local point of view of the system's agents, which are assumed to execute sequentially and to interact by means of synchronous event sharing. We present a sound and complete labelled tableaux system for full DTL. To achieve this, we first formalize a labelled tableaux system for reasoning locally at each agent and afterwards we combine the local systems into a global one by adding rules that capture the distributed nature of DTL. We also provide examples illustrating the use of DTL and our tableaux system.

TCTL Model Checking of Time Petri Nets

Boucheneb, H., Gardey, G., Roux, O. H. — Mon, 06 Jul 2009 22:54:04 PDT

We consider Time Petri Nets (TPN) for which a firing time interval is associated with each transition. State space abstractions for TPN preserving various classes of properties (LTL, CTL and CTL^_*) can be computed, in terms of so called state classes. Some methods were proposed to check quantitative timed properties but are not suitable for effective verification of properties of real-life systems. In this article, we consider subscript TCTL for TPN (TPN-TCTL) for which temporal operators are extended with a time interval, specifying a time constraint on the firing sequences. We prove the decidability of TPN-TCTL on bounded TPN and give its theoretical complexity. We propose a zone-based state space abstraction that preserves marking reachability and traces of the TPN. As for Timed Automata (TA), the abstraction may use an over-approximation operator on zones to enforce the termination. A coarser (and efficient) abstraction is then provided and proved exact w.r.t. marking reachability and traces (LTL properties). Finally, we consider a subset of TPN-TCTL properties (TPN-TCTLS) for which it is possible to propose efficient on-the-fly model-checking algorithms. Our approach consists in computing and exploring the zone-based state space abstraction. On a practical point of view, the method is integrated in Romeo [Gardey et al. (2005, Proceedings of 17th International Conference on CAV’05, Vol. 3576 of Lecture Notes in Computer Science, 418–423)], a tool for TPN edition and analysis. In addition to the old features it is now possible to effectively verify a subset of TCTL directly on TPN.

Nominal (Universal) Algebra: Equational Logic with Names and Binding

Gabbay, M. J., Mathijssen, A. — Sun, 05 Jul 2009 23:10:23 PDT

In informal mathematical discourse (such as the text of a paper on theoretical computer science), we often reason about equalities involving binding of object-variables. We find ourselves writing assertions involving meta-variables and captureavoidance constraints on where object-variables can and cannot occur free. Formalizing such assertions is problematic because the standard logical frameworks cannot express capture-avoidance constraints directly.

In this article, we make the case for extending the logic of equality with meta-variables and capture-avoidance constraints, to obtain ‘nominal algebra’. We use nominal techniques that allow for a direct formalization of meta-level assertions, while remaining close to informal practice. We investigate proof-theoretical properties, we provide a sound and complete semantics in nominal sets and we compare and contrast our design decisions with other possibilities leading to similar systems.

On Graph-theoretic Fibring of Logics

Sernadas, A., Sernadas, C., Rasga, J., Coniglio, M. — Sun, 05 Jul 2009 23:10:23 PDT

A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of two deductive systems is an m-graph whose nodes are language expressions and the m-edges represent the inference rules of the two original systems. The sobriety of the approach is confirmed by proving that all the fibring notions are universal constructions. This graph-theoretic view is general enough to accommodate very different fibrings of propositional based logics encompassing logics with non-deterministic semantics, logics with an algebraic semantics, logics with partial semantics and substructural logics, among others. Soundness and weak completeness are proved to be preserved under very general conditions. Strong completeness is also shown to be preserved under tighter conditions. In this setting, the collapsing problem appearing in several combinations of logic systems can be avoided.

On the Density of Truth of Locally Finite Logics

Kostrzycka, Z. — Fri, 26 Jun 2009 08:42:51 PDT

We prove that the density of truth exists for a large class of locally finite (locally tabular) propositional logics. We are primarily interested in classical and intuitionistic logic and show that their implicational fragments have the same density. There are also given some locally finite logics without the density of truth.

Towards a Common Framework for Dialectical Proof Procedures in Abstract Argumentation

Thang, P. M., Dung, P. M., Hung, N. D. — Fri, 26 Jun 2009 08:42:51 PDT

We present a common framework for dialectical proof procedures for computing credulous, grounded, ideal and sceptical preferred semantics of abstract argumentation. The framework is based on the notions of dispute derivation and base derivation. Dispute derivation is a dialectical notion first introduced for computing credulous semantics in assumption-based argumentation, and adapted here for computing credulous semantics and grounded semantics. Base derivation is introduced for two purposes: (i) to characterize all preferred extensions containing a given argument, and (ii) to represent backtracking in the search for a dispute derivation. We prove the soundness of the proof procedures for any argumentation frameworks and their completeness for general classes of finitary or finite-branching argumentation frameworks containing the class of finite argumentation frameworks as a subclass.We also discuss related results.

Logics Preserving Degrees of Truth from Varieties of Residuated Lattices

Bou, F., Esteva, F., Font, J. M., Gil, A. J., Godo, L., Torrens, A., Verdu, V. — Fri, 26 Jun 2009 08:42:50 PDT

Let K be a variety of (commutative, integral) residuated lattices. The substructural logic usually associated with K is an algebraizable logic that has K as its equivalent algebraic semantics, and is a logic that preserves truth, i.e. 1 is the only truth value preserved by the inferences of the logic. In this article, we introduce another logic associated with K, namely the logic that preserves degrees of truth, in the sense that it preserves lower bounds of truth values in inferences. We study this second logic mainly from the point of view of abstract algebraic logic. We determine its algebraic models and we classify it in the Leibniz and the Frege hierarchies: we show that it is always fully selfextensional, that for most varieties K it is non-protoalgebraic, and that it is algebraizable if and only K is a variety of generalized Heyting algebras, in which case it coincides with the logic that preserves truth. We also characterize the new logic in three ways: by a Hilbert style axiomatic system, by a Gentzen style sequent calculus and by a set of conditions on its closure operator. Concerning the relation between the two logics, we prove that the truth-preserving logic is the extension of the one that preserves degrees of truth with either the rule of Modus Ponens or the rule of Adjunction for the fusion connective.

Qualitative Temporal and Spatial Reasoning Revisited

Bodirsky, M., Chen, H. — Fri, 26 Jun 2009 08:42:50 PDT

Establishing local consistency is one of the main algorithmic techniques in temporal and spatial reasoning. Acentral question for the various proposed temporal and spatial constraint languages is whether local consistency implies global consistency. Showing that a constraint language has this ‘local-to-global’ property implies polynomial-time tractability of the constraint language, and has further pleasant algorithmic consequences. In the present article, we study the ‘local-to-global’ property by making use of a recently established connection of this property with universal algebra. Roughly speaking, the connection shows that this property is equivalent to the presence of a so-called quasi near-unanimity (QNU) polymorphism of the constraint language. We obtain new algorithmic results and give very concise proofs of previously known theorems. Our results concern well-known and heavily studied formalisms such as the point algebra, Allen's interval algebra and the spatial reasoning language RCC-5.

A Complete Deductive System for Probability Logic

Zhou, C. — Tue, 16 Jun 2009 06:22:12 PDT

In this article, we provide a complete deductive system ₊ for probability logic that is different from the systems by Fagin and Halpern and by Heifetz and Mongin in the literature. The most important principle of the axiomatization is an infinitary Archimedean rule (ARCH). Our proof of the completeness of ₊ is in keeping with the Kripke-style proof of completeness in modal logic. With the Fourier–Motzkin elimination method, we show both the decidability and Moss's conjecture that the rule (ARCH) is essentially finitary. The perspective of this article is mainly logical. At the end, we point to some further research continuing this piece of work from a coalgebraic perspective.

Property-based Slicing for Agent Verification

Bordini, R. H., Fisher, M., Wooldridge, M., Visser, W. — Tue, 16 Jun 2009 06:22:11 PDT

Programming languages designed specifically for multi-agent systems represent a new programming paradigm that has gained popularity over recent years, with some multi-agent programming languages being used in increasingly sophisticated applications, often in critical areas. To support this, we have developed a set of tools to allow the use of model-checking techniques in the verification of systems directly implemented in one particular language called AgentSpeak. The success of model checking as a verification technique for large software systems is dependent partly on its use in combination with various state-space reduction techniques, an important example of which is property-based slicing. This article introduces an algorithm for property-based slicing of AgentSpeak multi-agent systems. The algorithm uses literal dependence graphs, as developed for slicing logic programs, and generates a program slice whose state space is stuttering-equivalent to that of the original program; the slicing criterion is a property in a logic with LTL operators and (shallow) BDI modalities. In addition to showing correctness and characterizing the complexity of the slicing algorithm, we apply it to an AgentSpeak program based on autonomous planetary exploration rovers, and we discuss how slicing reduces the model-checking state space. The experiment results show a significant reduction in the state space required for model checking that agent, thus indicating that this approach can have an important impact on the future practicality of agent verification.

Residuated Lattices as an Algebraic Semantics for Paraconsistent Nelson's Logic

Busaniche, M., Cignoli, R. — Mon, 04 May 2009 00:14:44 PDT

The class of NPc-lattices is introduced as a quasivariety of commutative residuated lattices, and it is shown that the class of pairs (A,A⁺) such that A is an NPc-lattice and A⁺ is its positive cone, is a matrix semantics for Nelson paraconsistent logic.

Linear Temporal Logic LTLK extended by Multi-Agent Logic Kn with Interacting Agents

Rybakov, V. — Mon, 04 May 2009 00:14:43 PDT

We study an extension LTL_K of the linear temporal logic LTL_K by implementing multi-agent knowledge logic KD45_m (which is often referred as multi-modal logic S5_m). The temporal language of our logic adapts the operations U (until) and N (next) and uses new temporal operations: Uw—weak until, and Us—strong until. We also employ the standard agents’ knowledge operations K_i from the multi-agent logic KD45_m and extend them with an operation IntK responsible for knowledge obtained via interaction of agents. The semantic models for LTL_K are Kripke/Hintikka-like structures N_C based on the linear time. Structures N_C use i N as indexes for time, and the base set of any N_C consists of clusters C(i) (for all i N) containing all possible states at the time i. Agents’ knowledge is modelled in time clusters C(i) via agents’ knowledge accessibility relations R_j. The logic LTL_K is the set of all formulas which are valid (true) in all such models N_C w.r.t. all possible valuations. We prove that LTL_K is decidable: we reduce the decidability problem to verification of validity for special normal reduced forms of rules in specific models (not LTL_K models) of size single-exponential in size of the rules. Furthermore, we extend these results to a linear temporal logic LTL_K(Z) based on the time flow indexed by all integer numbers (with additional operations Since and Previous). Also we show that LTL_K has the finite model property (fmp) while LTL_K (Z) has no standard fmp.

The Non-classical Logics Corner of the Journal of Logic and Computation

Carnielli, W., Wansing, H. — Mon, 04 May 2009 00:14:43 PDT

A Graph-theoretic Account of Logics

Sernadas, A., Sernadas, C., Rasga, J., Coniglio, M. — Wed, 22 Apr 2009 06:00:33 PDT

A graph-theoretic account of logics is explored based on the general notion of m-graph (i.e; a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as multi-graphs (m-graphs). After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the approach our results apply to very different logics encompassing, among others, substructural logics as well as logics with non-deterministic semantics, and subsume all logics endowed with an algebraic semantics.

On the Logical Formalization of Possibilistic Counterparts of States over n-valued Lukasiewicz Events

Flaminio, T., Godo, L., Marchioni, E. — Thu, 26 Mar 2009 06:01:49 PDT

Possibility and necessity measures are commonly defined over Boolean algebras. This work considers a generalization of these kinds of measures over MV-algebras as a possibilistic counterpart of the (probabilistic) notion of state on MV-algebras. Two classes of possibilistic states over MV-algebras of functions are characterized in terms of (generalized) Sugeno integrals. For reasoning about these representable classes of possibilistic states, we introduce many-valued modal logics based on the Rational Lukasiewicz Logic, that are shown to be complete with respect to corresponding classes of Kripke models equipped with those states.

Modelling Judicial Context in Argumentation Frameworks

Wyner, A., Bench-Capon, T. — Thu, 26 Mar 2009 06:01:48 PDT

Much work using argumentation frameworks (AFs) treats arguments as entirely abstract, related by a uniform attack relation that always succeeds unless the attacker can itself be defeated. However, this does not seem adequate for legal argumentation. Some proposals have suggested regulating attack relations using preferences or values on arguments and that filter the attack relation, so that, depending on the audience addressed, some attacks fail and so can be removed from the framework. This does not, however, capture a central feature of legal reasoning: how a decision with respect to the same facts and legal reasoning varies as the judicial context varies. Nor does it capture related context-dependent features of legal reasoning, such as how an audience can prefer or value an argument, yet be constrained by precedent or authority not to accept it. Nor does it explain how certain types of attack may not be allowed in a particular procedural context. For this reason, evaluation of the status of arguments within a given framework must be allowed to depend not only on the attack relations along with the preference or value of arguments, but also on the nature of the attacks and the context in which they are made. We present a means to represent these features, enabling us to account for a number of factors currently considered to be beyond the remit of formal AFs. We give several examples of the use of approach including: appealing a case, overruling a precedent and rehearing of a case as a civil rather than criminal proceeding.

Editorial

Bench-Capon, T., Prakken, H. — Thu, 26 Mar 2009 06:01:47 PDT

The Logic of Acceptance: Grounding Institutions on Agents' Attitudes

Lorini, E., Longin, D., Gaudou, B., Herzig, A. — Thu, 26 Mar 2009 06:01:47 PDT

In the recent years, several formal approaches to the specification of normative multi-agent systems (MASs) and artificial institutions have been proposed. The aim of this article is to advance the state of the art in this area by proposing an approach in which a normative MAS is conceived to be autonomous, in the sense that it is able to create, maintain and eventually change its own institutions by itself, without the intervention of an external designer in this process. In our approach the existence and the dynamics of an institution (norms, rules, institutional facts, etc.) are determined by the (individual and collective) acceptances of its members, and its dynamics depends on the dynamics of these acceptances. In order to meet this objective, we propose the logic AL (Acceptance Logic) in which the acceptance of a proposition by the agents qua members of an institution is introduced. Such propositions are true w.r.t. an institutional context and correspond to facts that are instituted in an attitude-dependent way. The second part of the article is devoted to the logical characterization of some important notions in the theory of institutions. We provide a formalization of the concept of constitutive rule, expressed by a statement of the form ‘X counts as Y in the context of institution x’. Then, we formalize the concepts of obligation and permission (so called regulative rules). In our approach, constitutive rules and regulative rules of a certain institution are attitude-dependent facts which are grounded on the acceptances of the members of the institution.

Measures and Topologies on MV-algebras

Weber, H. — Wed, 18 Mar 2009 02:53:49 PDT

We present a topological approach to the study of measures on MV-algebras. These measures generalize, in the terminology of Butnariu and Klement (D. Butnariu and E. P. Klement. Triangular Norm based Measures and Games with Fuzzy Coalitions. Kluver, Dordrecht, 1993), T-valuations on clans of fuzzy sets.

Models for Many-Valued Probabilistic Reasoning

Flaminio, T., Montagna, F. — Wed, 18 Mar 2009 02:53:48 PDT

In this article, we compare models for many-valued probabilistic reasoning from the point of view of the sets of satisfiable formulas, positive satisfiable formulas, and tautologies. The results arising from this comparison will be used in the final part of the present article to provide results about the computational complexity for the problem of deciding if a formula belongs to one of the previously discussed sets.

On States on MV-algebras and their Applications

Dvurecenskij, A. — Wed, 18 Mar 2009 02:53:48 PDT

We present the notion of a state, as averaging or a probabilistic assessment in many-valued reasoning. We show what a state can be in different algebraic structures, and also present a new trends using de Finetti's coherence principle or state MV-algebras where the state is an internal notion.

State Smearing Theorems and the Existence of States on Some Atomic Lattice Effect Algebras

Riecanova, Z., Paseka, J. — Fri, 13 Mar 2009 03:17:22 PDT

The existence of states and probabilities on effect algebras as logical structures when events may be non-compatible, unsharp, fuzzy or imprecise is still an open question. Only a few families of effect algebras possessing states are known. We are going to show some families of effect algebras, the existence of a pseudocomplementation on which implies the existence of states. Namely, those are Archimedean atomic lattice effect algebras, which are sharply dominating or s-compactly generated or extendable to complete lattice effect algebras.

A Compact [0,1]-valued First-order Lukasiewicz Logic with Identity on Hilbert Space

Mundici, D. — Fri, 13 Mar 2009 03:17:20 PDT

By an MV-set, we understand a pair (E,X) where X is a set of unit vectors in a Hilbert space E such that the linear span of X is dense in E, and <v,w> ≥ 0 for all v,w X. The scalar product <v,w> [0,1] is the identity degree of v and w. Building on MV-sets and continuous functions and relations defined on them, we construct a compact [0,1]-valued first-order Lukasiewicz logic, whose set of unsatisfiable formulas is recursively enumerable. In the particular case when X is an orthonormal basis of E we recover classical Skolem first-order logic with identity, constants, functions and relations. Our main tools are the Kolmogorov dilation theorem for positive semidefinite kernels, and the Tarski–Seidenberg decision method for elementary algebra and geometry.

States on Bold Algebras: Categorical Aspects

Fric, R. — Fri, 13 Mar 2009 03:17:19 PDT

We study bold algebras and states on bold algebras in the context of transition from classical probability theory to fuzzy probability theory. Our aim is to point out the role of bold algebras and states on bold algebras in a categorical approach to probability theory. In particular, we formulate several fundamental questions related to basic probability notions and constructions and provide possible answers in terms of bold algebras and states on bold algebras. We show that the category ID of D-posets of fuzzy sets and sequentially continuous difference homomorphisms can serve as a base category in which both classical and fuzzy probability theory can be developed and generalized. Classical and fuzzy random events such as fields of sets and measurable real-valued functions into the interval [0,1], considered as bold algebras, become special objects. Observables, considered as morphisms between objects, become dual to generalized random variables. States become morphisms into [0,1], considered as an object of ID. Properties of objects of ID follow from classical theorems of analysis such as the Lebesgue Dominated Convergence Theorem (states are sequentially continuous) and categorical constructions such as the product (the structure of a probability domain is completely determined by the states as the initial structure). We prove that each generated Lukasiewicz tribe is the epireflection of its underlying Butnariu–Klement -field of sets. This helps to understand the transition from classical crisp random events to fuzzy random events. Indeed, the corresponding fuzzification is necessary to cover generalized random variables having a quantum character, i.e. fuzzy random variables in the Gudder–Bugajski sense sending a classical elementary event (point measure) to a non-trivial probability measure.

Core of Coalition Games on MV-algebras

Kroupa, T. — Thu, 12 Mar 2009 00:38:34 PDT

Coalition games are generalized to semisimple MV-algebras. Coalitions are viewed as [0, 1]-valued functions on a set of players, which enables to express a degree of membership of a player in a coalition. Every game is a real-valued mapping on a semisimple MV-algebra. The goal is to recover the so-called core: a set of final distributions of payoffs, which are represented by measures on the MV-algebra. A class of sublinear games are shown to have a non-empty core and the core is completely characterized in certain special cases. The interpretation of games on propositional formulas in Lukasiewicz logic is introduced.

On a Finitely Axiomatizable Kripke Incomplete Logic Containing KTB

Kostrzycka, Z. — Tue, 10 Mar 2009 21:57:14 PDT

We construct a finite extension of T₂ = KTB²p->³p which is Kripke incomplete.

Metric Completions of MV-algebras with States: An Approach to Stochastic Independence

Leustean, I. — Tue, 10 Mar 2009 21:57:13 PDT

The state theory on MV-algebras is a generalization of Boolean probability theory and is a counterpart of the theory of states defined on lattice-ordered groups. We first investigate the metric space naturally associated to an MV-algebra with a state. The metric completion of anMV-algebra is defined and characterized in relation with the geometric properties of the corresponding state. We propose a concept of independent probability MV-algebras, attempting to solve an open problem from Riecan and Mundici.

A Database Approach to Distributed State-Space Generation

Blom, S., Lisser, B., Van De Pol, J., Weber, M. — Thu, 05 Mar 2009 01:40:06 PST

We study distributed state-space generation on a cluster of workstations. It is explained why state-space partitioning by a global hash function is problematic when states contain variables from unbounded domains, such as lists or other recursive data types. Our solution is to introduce a database which maintains a global numbering of state values. We also describe tree compression, a technique of recursive state folding, and show that it is superior to manipulating plain state vectors. This solution is implemented and linked to the µCRL toolset, where state values are implemented as maximally shared terms (ATerms). However, it is applicable to other models as well, e.g. PROMELA or LOTOS models. Our experiments show the trade-offs between keeping the database global, replicated or local, depending on the available network bandwidth and latency.

An Axiomatic System Suggested by Quantum Computation

Bertini, C., Leporini, R. — Fri, 27 Feb 2009 04:38:23 PST

The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister (a system of qubits in a pure state) or, more generally, with a mixture of quregisters (called qumix). Following an approach proposed by Domenech and Freytes, we apply residuated structures associated with fuzzy logic to develop certain aspects of information processing in quantum computing from a logical perspective. For this purpose, we introduce an axiomatic system whose natural interpretation is the irreversible quantum Poincaré algebra. Such a system allows to establish a completeness theorem.

Comparing LTL Semantics for Runtime Verification

Bauer, A., Leucker, M., Schallhart, C. — Thu, 26 Feb 2009 07:40:32 PST

When monitoring a system w.r.t. a property defined in a temporal logic such as LTL, a major concern is to settle with an adequate interpretation of observable system events; that is, models of temporal logic formulae are usually infinite words of events, whereas at runtime only finite but incrementally expanding prefixes are available.

In this work, we review LTL-derived logics for finite traces from a runtime-verification perspective. In doing so, we establish four maxims to be satisfied by any LTL-derived logic aimed at runtime verification. As no pre-existing logic readily satisfies all of them, we introduce a new four-valued logic Runtime Verification Linear Temporal Logic RV-LTL in accordance to these maxims. The semantics of Runtime Verification Linear Temporal Logic (RV-LTL) indicates whether a finite word describes a system behaviour which either (i) satisfies the monitored property, (ii) violates the property, (iii) will presumably violate the property, or (iv) will presumably conform to the property in the future, once the system has stabilized. Notably, (i) and (ii) correspond to the classical semantics of LTL, whereas (iii) and (iv) are chosen whenever an observed system behaviour has not yet lead to a violation or acceptance of the monitored property.

Moreover, we present a monitor construction for RV-LTL properties in terms of Moore machines signalizing the semantics of the so far obtained execution trace w.r.t. the monitored property.

Speculative Image Computation for Distributed Symbolic Reachability Analysis

Chung, M.-Y., Ciardo, G. — Fri, 20 Feb 2009 22:31:19 PST

The Saturation-style fixpoint iteration strategy for symbolic reachability analysis is particularly effective for globally asynchronous locally synchronous discrete-state systems. However, its inherently sequential nature makes it difficult to parallelize Saturation on a network workstations (NOW). We then propose the idea of using idle workstation time to perform speculative image computations. Since an unrestrained prediction may make excessive use of computational resources, we introduce a history-based approach to dynamically recognize image computation (event firing) patterns and explore only firings that conform to these patterns. In addition, we employ an implicit encoding for the patterns, so that the actual image computation history can be efficiently preserved. Experiments not only show that image speculation works on a realistic model, but also indicate that the use of an implicit encoding together with two heuristics results in a better informed speculation.

Distributed Algorithms for SCC Decomposition

Barnat, J., Chaloupka, J., Van De Pol, J. — Tue, 17 Feb 2009 04:49:21 PST

We study existing parallel algorithms for the decomposition of a partitioned graph into its strongly connected components (SCCs). In particular, we identify several individual procedures that the algorithms are assembled from and show how to assemble a new and more efficient algorithm, called Recursive OBF (OBFR), to solve the decomposition problem. We also report on a thorough experimental study to evaluate the new algorithm. It shows that it is possible to perform SCC decomposition in parallel efficiently and that OBFR, if properly implemented, is the best choice in most cases.

To Parallelize or to Optimize?

Ezekiel, J., Luttgen, G., Siminiceanu, R. — Thu, 12 Feb 2009 06:09:44 PST

Model checking is a popular and successful technique for verifying complex digital systems. Carrying this technique—and its underlying state-space generation algorithms—beyond its current limitations presents itself with a number of alternatives. Our focus is on parallelization which is made attractive by the current trend in hardware architectures towards multi-core, multi-processor systems. The main obstacle in this endeavour is that, in particular, symbolic state-space generation algorithms are notoriously hard to parallelize. In this article, we describe the process of taking a sequential symbolic state-space generation algorithm, namely a generic, symbolic BFS algorithm, through a sequence of optimizations that leads up to the Saturation algorithm and follow the impact these sequential algorithms have on their parallel counterparts. In particular, we develop a parallel version of Saturation, discuss the challenges faced in its design and conduct extensive experimental studies of its implementation. We employ rigorous analysis tools and techniques for measuring and evaluating parallel overheads and the quality of the parallelization. The outcome of these studies is that the performance of a parallel symbolic state-space generation algorithm is almost impossible to predict and highly dependent on the model to which it is applied. In most situations, perceivable speed-ups are hard to achieve, but real-world applications where our technique produces significant improvements do exist. Nevertheless, it appears that time is better invested in optimizing sequential symbolic model checking algorithms rather than parallelizing them.

Presentation of Set Functors: A Coalgebraic Perspective

Adamek, J., Gumm, H. P., Trnkova, V. — Thu, 12 Feb 2009 06:09:43 PST

Accessible set functors can be presented by signatures and equations as quotients of polynomial functors.We determine how preservation of pullbacks and other related properties (often applied in coalgebra) are reflected in the structure of the system of equations.

Parallel SAT Solving in Bounded Model Checking

Abraham, E., Schubert, T., Becker, B., Franzle, M., Herde, C. — Mon, 09 Feb 2009 01:59:17 PST

Bounded model checking (BMC) is an incremental refutation technique to search for counterexamples of increasing length. The existence of a counterexample of a fixed length is expressed by a first-order logic formula that is checked for satisfiability using a suitable solver. We apply communicating parallel solvers to check satisfiability of the BMC formulae. In contrast to other parallel solving techniques, our method does not parallelize the satisfiability check of a single formula, but the parallel solvers work on formulae for different counterexample lengths. We adapt the method of constraint sharing and replication of Shtrichman, originally developed for sequential BMC, to the parallel setting. Since the learning mechanism is now parallelized, it is not obvious whether there is a benefit from the concepts of Shtrichman in the parallel setting. We demonstrate on a number of benchmarks that adequate communication between the parallel solvers yields the desired results.

Exemplaric Expressivity of Modal Logics

Jacobs, B., Sokolova, A. — Tue, 03 Feb 2009 04:24:44 PST

This article investigates expressivity of modal logics for transition systems, multitransition systems, Markov chains and Markov processes, as coalgebras of the powerset, finitely supported multiset, finitely supported distribution and measure functor, respectively. Expressivity means that logically indistinguishable states, satisfying the same formulas, are behaviourally indistinguishable. The investigation is based on the framework of dual adjunctions between spaces and logics and focuses on a crucial injectivity property. The approach is generic both in the choice of systems and modalities, and in the choice of a ‘base logic’. Most of these expressivity results are already known, but the applicability of the uniform setting of dual adjunctions to these particular examples is what constitutes the contribution of the article.

Proof Theory Corner

Avron, A. — Thu, 22 Jan 2009 06:12:13 PST

Sequent Calculi for the Modal {micro}-Calculus over S5

Alberucci, L. — Thu, 22 Jan 2009 06:12:12 PST

We present two sequent calculi for the modal µ-calculus over S5 and prove their completeness by using classical methods. One sequent calculus has an analytical cut rule and could be used for a decision procedure the other uses a modified version of the induction rule.We also provide a completeness theorem for Kozen's Axiomatization over S5 without using the completeness result established byWalukiewicz for the modal µ-calculus over arbitrary models.

Model-theoretic and Computational Properties of Modal Dependence Logic

Sevenster, M. — Tue, 20 Jan 2009 23:21:21 PST

We study the basic modal language extended by an operator dep. If p_i are propositional atoms, then dep(p₁,...,p_n_–1;p_n) expresses, intuitively, that p_n only depends on p₁,...,p_n_–1. The resulting language was baptized ‘modal dependence logic’ by Väänänen in his paper Modal Dependence Logic. The current article compares modal dependence logic with basic modal logic in terms of its model-theoretic and computational properties. We show that modal dependence logic is strictly more expressive than modal logic, but that under special conditions modal dependence logic can be translated into basic modal logic.We show that the complexity of modal dependence logic is NEXP-complete.

Interpolation Properties, Beth Definability Properties and Amalgamation Properties for Substructural Logics

Kihara, H., Ono, H. — Thu, 08 Jan 2009 05:14:35 PST

This article develops a comprehensive study of various types of interpolation properties and Beth definability properties (BDPs) for substructural logics, and their algebraic characterizations through amalgamation properties (APs) and epimorphisms surjectivity. In general, substructural logics are algebraizable but lack many of the basic logical properties that modal and superintuitionistic logics enjoy [Gabbay and Maksimova (2005, Oxford Logic Guides, Vol. 46)]. In this case, careful examination is necessary to see how these logical and algebraic properties are related. To describe these relations exactly, many variants of interpolation properties and BDPs, and also corresponding algebraic properties, are introduced. Because of their generality, the results reported here hold not only for substructural logics, but can also be extended to a more general setting such as abstract algebraic logic [Andréka, Németi and Sain (Handbook of Philosophical Logic, Vol. 2, 2nd edn, pp. 133–247) and Czelakowski and Pigozzi (1999, Vol. 203 of Lecture Notes in Pure and Applied Mathematics, pp. 187–265)].

Tableaux and Resource Graphs for Separation Logic

Galmiche, D., Mery, D. — Thu, 08 Jan 2009 05:14:35 PST

Separation logic (SL) is often presented as an assertion language for reasoning about mutable data structures. As recent results about verification in SL have mainly been achieved from a model-checking point of view, our aim in this article is to study SL from a complementary proof-theoretic perspective in order to provide results about proof search in SL. We begin our study with a fragment of SL, denoted SLP, where first-order quantifiers, variables and equality are removed. We first define specific structures, called resource graphs, that capture SLP models by considering heaps as resources via a labelling process. We then provide a tableau calculus that allows us to build such resource graphs from which either proofs, or countermodels can be generated. We finally prove soundess, completeness and termination of our tableau calculus before discussing extensions to various fragments of SL (including full SL) and the related decidability issues.

Tableaux for Logics of Subinterval Structures over Dense Orderings

Bresolin, D., Goranko, V., Montanari, A., Sala, P. — Tue, 23 Dec 2008 23:31:34 PST

In this article, we develop tableau-based decision procedures for the logics of subinterval structures over dense linear orderings. In particular, we consider the two difficult cases: the relation of strict subintervals (with both endpoints strictly inside the current interval) and the relation of proper subintervals (that can share one endpoint with the current interval). For each of these logics, we establish a small pseudo-model property and construct a sound, complete and terminating tableau that searches systematically for existence of such a pseudo-model satisfying the input formulas. Both constructions are non-trivial, but the latter is substantially more complicated because of the presence of beginning and ending subintervals which require special treatment. We prove PSPACE completeness for both procedures and implement them in the generic tableau-based theorem prover Lotrec.

A Note on Expressive Coalgebraic Logics for Finitary Set Functors

Moss, L. S. — Mon, 22 Dec 2008 00:59:14 PST

This article has two purposes. The first is to present a final coalgebra construction for finitary endofunctors on Set that uses a certain subset L* of the limit L of the first terms in the final sequence. L* is the set of points in L which arise from all coalgebras using their canonical morphisms into L, and it was used earlier for different purposes in Kurz and Pattinson (2005, Mathematical Structures in Computer Science, 15, 543–473). Viglizzo (2005, PhD Dessertation, Indiana University) showed that the same set L* carried a final coalgebra structure for functors in a certain inductively defined family. Our first goal is to generalize this to all finitary endofunctors; the result is implicit in Worrell (2005, Theoritical Computer Science, 338, 184–199). The second goal is to use the final coalgebra construction to propose coalgebraic logics similar to those in Lawrence S. Moss (1999, Annals of Pure and Applied Logic, 96, 277–317) but for all finitary endofunctors F on Set. This time one can dispense with all conditions on F, construct a logical language L_F directly from it, and prove that two points in a coalgebra satisfy the same sentences of L_F iff they are identified by the final coalgebra morphism. The language L_F is very spare, having no boolean connectives. This work on L_F is thus a re-working of coalgebraic logic for finitary functors on sets.

Vietoris Bisimulations

Bezhanishvili, N., Fontaine, G., Venema, Y. — Mon, 22 Dec 2008 00:59:14 PST

Building on the fact that descriptive frames are coalgebras for the Vietoris functor on the category of Stone spaces, we introduce and study the concept of a Vietoris bisimulation between two descriptive modal models, together with the associated notion of bisimilarity. We prove that our notion of bisimilarity, which is defined in terms of relation lifting, coincides with Kripke bisimilarity (with respect to the underlying Kripke models), with behavioural equivalence, and with modal equivalence, but not with Aczel–Mendler bisimilarity. As a corollary, we obtain that the Vietoris functor does not preserve weak pullbacks. Comparing Vietoris bisimulations between descriptive models to Kripke bisimulations on the underlying Kripke models, we prove that the closure of such a Kripke bisimulation is a Vietoris bisimulation. As a corollary, we show that the collection of Vietoris bisimulations between two descriptive models forms a complete lattice. Finally, we provide a game-theoretic characterization of Vietoris bisimilarity.

Quantale Modules and their Operators, with Applications

Russo, C. — Mon, 22 Dec 2008 00:59:13 PST

The central topic of this work is the categories of modules over unital quantales. The main categorical properties are established and a special class of operators, called Q-module transforms, is defined. Such operators—that turn out to be precisely the homomorphisms between free objects in those categories—find concrete applications in two different branches of image processing, namely fuzzy image compression and mathematical morphology.

Categorical Equivalences for Formula quasi-MV Algebras

Giuntini, R., Paoli, F., Ledda, A. — Mon, 22 Dec 2008 01:46:05 PST

In previous investigations into the subject [Giuntini et al. (2007, Studia Logica, 87, 99–128), Paoli et al. (2008, Reports on Mathematical Logic, 44, 53–85), Bou et al. (2008, Soft Computing, 12, 341–352)], $$\sqrt{\text{'}}$$ quasi-MV algebras have been mainly viewed as preordered structures w.r.t. the induced preorder relation of their quasi-MV term reducts. In this article, we shall focus on a different relation which partially orders cartesian $$\sqrt{\text{'}}$$ quasi-MV algebras. We shall prove that: (i) every cartesian $$\sqrt{\text{'}}$$ quasi-MV algebra is embeddable into an interval in a particular Abelian -group with operators; (ii) the category of cartesian $$\sqrt{\text{'}}$$ quasi-MV algebras isomorphic with the pair algebras over their own polynomial MV subreducts is equivalent both to the category of such -groups (with strong order unit), and to the category of MV algebras. As a by-product of these results we obtain a purely group-theoretical equivalence, namely between the mentioned category of -groups with operators and the category of Abelian -groups (both with strong order unit).

Rank-1 Modal Logics are Coalgebraic

Schroder, L., Pattinson, D. — Wed, 17 Dec 2008 04:37:37 PST

Coalgebras provide a unifying semantic framework for a wide variety of modal logics. It has previously been shown that the class of coalgebras for an endofunctor can always be axiomatized in rank 1. Here we establish the converse, i.e. every rank-1 modal logic has a sound and strongly complete coalgebraic semantics. This is achieved by constructing for a given modal logic a canonical coalgebraic semantics, consisting of a signature functor and interpretations of modal operators, which turns out to be final among all such structures. The canonical semantics may be seen as a coalgebraic reconstruction of neighbourhood semantics, broadly construed. A finitary restriction of the canonical semantics yields a canonical weakly complete semantics which moreover enjoys the Hennessy–Milner property. As a consequence, the machinery of coalgebraic modal logic, in particular generic decision procedures and upper complexity bounds, becomes applicable to arbitrary rank-1 modal logics, without regard to their semantic status; we thus obtain purely syntactic versions of such results. As an extended example, we apply our framework to recently defined deontic logics. In particular, our methods lead to the new result that these logics are strongly complete.

Deduction Systems for Coalgebras Over Measurable Spaces

Goldblatt, R. — Fri, 12 Dec 2008 03:55:03 PST

A theory of infinitary deduction systems is developed for the modal logic of coalgebras for measurable polynomial functors on the category of measurable spaces. These functors have been shown by Moss and Viglizzo to have final coalgebras that represent certain universal type spaces in game-theoretic economics. A notable feature of the deductive machinery is an infinitary Countable Additivity Rule. A deductive construction of canonical spaces and coalgebras leads to completeness results. These give a proof-theoretic characterization of the semantic consequence relation for the logic of any measurable polynomial functor as the least deduction system satisfying Lindenbaum's Lemma. It is also the only Lindenbaum system that is sound. The theory is additionally worked out for Kripke polynomial functors, on the category of sets, that have infinite constant sets in their formation.

Constructive Logic with Strong Negation as a Substructural Logic

Busaniche, M., Cignoli, R. — Fri, 12 Dec 2008 03:55:02 PST

Spinks and Veroff have shown that constructive logic with strong negation (CLSN for short), can be considered as a substructural logic. We use algebraic tools developed to study substructural logics to investigate some axiomatic extensions of CLSN. For instance, we prove that Nilpotent minimum logic is the extension of CLSN by the prelinearity axiom. This generalizes the well-known result by Monteiro and Vakarelov that three-valued Lukasiewicz logic is an extension of CLSN. A Glivenko-like theorem relating CLSN and three-valued Lukasiewicz logic is proved.

The Hyper Tableaux Calculus with Equality and an Application to Finite Model Computation

Baumgartner, P., Furbach, U., Pelzer, B. — Sat, 06 Dec 2008 04:26:38 PST

In most theorem proving applications, a proper treatment of equational theories or equality is mandatory. In this article we show how to integrate a modern treatment of equality in the hyper tableau calculus. It is based on splitting of positive clauses and an adapted version of the superposition inference rule, where equations used for superposition are drawn (only) from a set of positive unit clauses, and superposition inferences into positive literals is restricted into (positive) unit clauses only. The calculus also features a generic, semantically justified simplification rule which covers many redundancy elimination techniques known from superposition theorem proving. Our main results are soundness and completeness of the calculus, but we also show how to apply the calculus for finite model computation, and we briefly describe the implementation.

Differential-algebraic Dynamic Logic for Differential-algebraic Programs

Platzer, A. — Fri, 05 Dec 2008 03:40:27 PST

We generalize dynamic logic to a logic for differential-algebraic (DA) programs, i.e. discrete programs augmented with first-order differential-algebraic formulas as continuous evolution constraints in addition to first-order discrete jump formulas. These programs characterize interacting discrete and continuous dynamics of hybrid systems elegantly and uniformly. For our logic, we introduce a calculus over real arithmetic with discrete induction and a new differential induction with which DA programs can be verified by exploiting their differential constraints algebraically without having to solve them. We develop the theory of differential induction and differential refinement and analyse their deductive power. As a case study, we present parametric tangential roundabout maneuvers in air traffic control and prove collision avoidance in our calculus.

Applying Universal Algebra to Lambda Calculus

Manzonetto, G., Salibra, A. — Thu, 27 Nov 2008 04:35:37 PST

The aim of this article is double. From one side we survey the knowledge we have acquired these last ten years about the lattice of all -theories (equational extensions of untyped -calculus) and the models of lambda calculus via universal algebra. This includes positive or negative answers to several questions raised in these years as well as several independent results, the state of the art about the long-standing open questions concerning the representability of -theories as theories of models, and 26 open problems. On the other side, against the common belief, we show that lambda calculus and combinatory logic satisfy interesting algebraic properties. In fact the Stone representation theorem for Boolean algebras can be generalized to combinatory algebras and -abstraction algebras. In every combinatory and -abstraction algebra, there is a Boolean algebra of central elements (playing the role of idempotent elements in rings). Central elements are used to represent any combinatory and -abstraction algebra as a weak Boolean product of directly indecomposable algebras (i.e. algebras that cannot be decomposed as the Cartesian product of two other non-trivial algebras). Central elements are also used to provide applications of the representation theorem to lambda calculus. We show that the indecomposable semantics (i.e. the semantics of lambda calculus given in terms of models of lambda calculus, which are directly indecomposable as combinatory algebras) includes the continuous, stable and strongly stable semantics, and the term models of all semisensible -theories. In one of the main results of the article we show that the indecomposable semantics is equationally incomplete, and this incompleteness is as wide as possible.

Collaborative Runtime Verification with Tracematches

Bodden, E., Hendren, L., Lam, P., Lhotak, O., Naeem, N. A. — Thu, 27 Nov 2008 04:35:37 PST

Perfect pre-deployment test coverage is notoriously difficult to achieve for large applications. Given enough end users, however, many more test cases will be encountered during an application's deployment than during testing. The use of runtime verification after deployment would enable developers to detect unexpected situations. Unfortunately, the prohibitive performance cost of runtime monitors prevents their use in deployed code. In this work, we study the feasibility of collaborative runtime verification, a verification approach which can distribute the burden of runtime verification among multiple users and over multiple runs. Each user executes a partially instrumented program and therefore suffers only a fraction of the instrumentation overhead. We focus on runtime verification using tracematches. Tracematches are a specification formalism that allows users to specify runtime verification properties via regular expressions with free variables over the dynamic execution trace. We propose two techniques for soundly partitioning the instrumentation required for tracematches: spatial partitioning, where different copies of a program monitor different program points for violations, and temporal partitioning, where monitoring is switched on and off over time. We evaluate the relative impact of partitioning on a user's runtime overhead by applying each partitioning technique to a collection of benchmarks that would otherwise incur significant instrumentation overhead. Our results show that spatial partitioning almost completely eliminates runtime overhead (for any particular benchmark copy) on many of our test cases, and that temporal partitioning scales well and provides runtime verification on a ‘pay as you go’ basis.

Syllogistic Logics with Verbs

Moss, L. S. — Wed, 26 Nov 2008 04:50:07 PST

This article provides sound and complete logical systems for several fragments of English which go beyond syllogistic logic in that they use verbs as well as other limited syntactic material: universally and existentially quantified noun phrases, building on the work of Nishihara, Morita and Iwata (1990, Systems and Computers in Japan, 21, 96–111); complemented noun phrases, following our Moss (2007, Syllogistic Logic with Complements); and noun phrases which might contain relative clauses, recursively, based on McAllester and Givan (1992, Artifical Intelligence, 56, 1–20). The logics are all syllogistic in the sense that they do not make use of individual variables. Variables in our systems range over nouns, and in the last system, over verbs as well.

Solutions to Some Open Problems on Totally Ordered Monoids

Horcik, R. — Wed, 26 Nov 2008 04:50:06 PST

In this article, solutions to three open problems on ordered commutative monoids posed in Evans et al. (2001, Semigroup forum, 62, 249-278) [4] are presented. By an ordered monoid, we always mean a totally ordered monoid. All the problems are related to the class of ordered commutative monoids which are homomorphic images of ordered free commutative monoids.

Rule Systems for Run-time Monitoring: from EAGLE to RULER

Barringer, H., Rydeheard, D., Havelund, K. — Fri, 21 Nov 2008 04:12:52 PST

In Barringer et al. (2004,Vol. 2937, LNCS), Eagle was introduced as a general purpose rule-based temporal logic for specifying run-time monitors. A novel interpretative trace-checking scheme via stepwise transformation of an Eagle monitoring formula was defined and implemented. However, even though Eagle presents an elegant formalism for the expression of complex trace properties, Eagle's interpretation scheme is complex and appears difficult to implement efficiently. In this article, we introduce RuleR, a primitive conditional rule-based system, which has a simple and easily implemented algorithm for effective run-time checking, and into which one can compile a wide range of temporal logics and other specification formalisms used for run-time verification. As a formal demonstration, we provide a translation scheme for linear-time propositional temporal logic with a proof of translation correctness. We then introduce a parameterized version of RuleR, in which rule names may have rule-expression or data parameters, which then coincides with the same expressivity as Eagle with data arguments. RuleR with just rule-expression parameters extend the expressiveness of RuleR strictly beyond the class of context-free languages. For the language classes expressible in propositional RuleR, the addition of rule-expression and data parameters enables more compact translations. Finally, we outline a few simple syntactic extensions of ‘core’ RuleR that can lead to further conciseness of specification but still enabling easy and efficient implementation.

Tableaux for Public Announcement Logic

Balbiani, P., Van Ditmarsch, H., Herzig, A., De Lima, T. — Fri, 21 Nov 2008 04:12:50 PST

Public announcement logic extends multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. In this article, we propose a labelled tableau calculus for this logic, and show that it decides satisfiability of formulas in deterministic polynomial space. Since this problem is known to be PSPACE-complete, it follows that our proof method is optimal.

A Non-finitary Sentential Logic that is Elementarily Algebraizable

Raftery, J.G. — Thu, 20 Nov 2008 04:36:27 PST

We exhibit a non-finitary sentential logic that is algebraized by a quasivariety—in fact by a finitely based variety of finite type. The algebraization process requires infinitely many defining equations. The existence of such a logic settles a question posed in Czelakowski (2001, Protoalgebraic Logics) and implicit in Herrmann (1996, Studia Logica, 57, 419–436).

Reduced Implicate Tries with Updates

Murray, N. V., Rosenthal, E. — Thu, 20 Nov 2008 04:36:27 PST

The reduced implicate trie, introduced in Murray and Rosenthal (2005, Vol. 3702 of Lecture Notes in Artifical Intelligence, pp. 231–244), is a data structure that may be used as a target language for knowledge compilation. It has the property that, even when large, it guarantees fast response to queries. Specifically, a query can be processed in time linear in the size of the query regardless of the size of the compiled knowledge base. The knowledge compilation paradigm typically assumes that the ‘intractable part’ of the processing be done once, during compilation. This assumption could render updating the knowledge base infeasible if recompilation is required. The ability to install updates without recompilation may therefore considerably widen applicability. In this article, several update operations not requiring recompilation are developed. These include disjunction, substitution of truth constants, conjunction with unit clauses, reordering of variables and conjunction with arbitrary clauses.

Temporal Assertions with Parametrized Propositions

Stolz, V. — Mon, 17 Nov 2008 20:03:28 PST

We extend our previous approach to run-time verification of a single finite path against a formula in next-free Linear-Time Logic (LTL) with free variables and quantification. We discuss the design space of quantification and introduce a binary operator that binds values based on the current state. The binding semantics of propositions containing quantified variables is a pure top-down evaluation. The alternating binding automaton corresponding to a formula is evaluated in a breadth-first manner, allowing us to detect refuted formulae during execution.

A New Method to Obtain Termination in Backward Proof Search For Modal Logic S4

Pliuskevicius, R., Pliuskeviciene, A. — Mon, 17 Nov 2008 20:03:27 PST

It is well known that problem of cycles starts up in tableau- or sequent-based decision procedures for S4 and a number of other modal logics. Traditional techniques used to ensure termination of algorithms for backward proof search in such modal logics are based on loop check. Since unrestricted loop check requires quite involved implementation techniques, effective loop check methods have been proposed. These methods are mainly based using the notion of history that involves a compact information about some previous parts of backward proof search. In the article a new method to obtain termination in backward proof search for modal logic S4 is proposed. This method is based on loop check-free sequent calculus and does not require any form history. Using this method translation of sequents into a certain normal form is not utilized. Instead of histories, we use marks and indices with the help of which applications of modal rules (namely, transitivity and reflexivity rules) are restricted. Instead of an unrestricted transitivity rule in the usual sequent calculus for S4 several transitivity rules (corresponding to specific positive occurrences of the necessity modality) are introduced. The peculiarities of the introduced transitivity rules along with proposed complete strategy of their application allow us to eliminate loop check and to restrict backtracking in derivations. By relying on the constructed loop check-free sequent calculus a Pspace procedure for determination of termination of backward proof search in modal logic S4 is presented.

Herbrand's Theorem, Skolemization and Proof Systems for First-Order Lukasiewicz Logic

Baaz, M., Metcalfe, G. — Mon, 17 Nov 2008 20:03:27 PST

An approximate Herbrand theorem is established for first-order infinite-valued Lukasiewicz Logic and used to obtain a proof-theoretic proof of Skolemization. These results are then used to define proof systems in the framework of hypersequents. In particular, a calculus lacking cut elimination is defined for the first-order logic characterized by linearly ordered MV-algebras, a cut-free calculus with an infinitary rule for the full first-order Lukasiewicz Logic, and a cut-free calculus with finitary rules for its one-variable fragment.

Interaction-based Runtime Verification for Systems of Systems Integration

Kruger, I. H., Meisinger, M., Menarini, M. — Sun, 16 Nov 2008 20:41:49 PST

Complex distributed systems pose great challenges for quality assurance. Size, complexity and concurrency of these systems often render traditional verification techniques impractical. In particular, this is true for systems integration efforts, where additional challenges arise from the independent evolution of the composed systems. Runtime verification provides a systematic strategy for analytical quality assurance of such systems. Key elements of runtime verification are system models, ways to inject these models into the observed system and a framework for analysing and monitoring the runtime behaviour against the models. The approach we present in this article is based on interaction models. We specify expected system interactions using Message Sequence Charts (MSC), from which we generate distributed runtime monitors for each of the components. We use aspect-oriented programming (AOP) techniques to inject the monitors into the implementation of the components. Thereby, we verify the adherence of the distributed system interactions with the MSC model. The focus of this article is the runtime verification in the systems integration domain; here, Enterprise Service Buses (ESB) have emerged as a powerful infrastructure for integrating complex distributed systems. In the context of an ESB we leverage the Spring AOP framework to inject the runtime monitors. As a result we obtain a comprehensive, tool-supported approach for model-based runtime verification of interactions. We demonstrate our approach using the Central Locking System as running example of an integrated embedded system.

Combining Derivations and Refutations for Cut-free Completeness in Bi-intuitionistic Logic

Gore, R., Postniece, L. — Sun, 16 Nov 2008 20:41:49 PST

Bi-intuitionistic logic is the union of intuitionistic and dual intuitionistic logic, and was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her subsequent ‘cut-free’ sequent calculus has recently been shown to fail cut-elimination. We present a new cut-free sequent calculus for bi-intuitionistic logic, and prove it sound and complete with respect to its Kripke semantics. Ensuring completeness is complicated by the interaction between intuitionistic implication and dual intuitionistic exclusion, similarly to future and past modalities in tense logic. Our calculus handles this interaction using derivations and refutations as first class citizens. We employ extended sequents which pass information from premises to conclusions using variables instantiated at the leaves of refutations, and rules which compose certain refutations and derivations to form derivations. Automated deduction using terminating backward search is also possible, although this is not our main purpose.

Analytic Methods for the Logic of Proofs

Finger, M. — Sun, 16 Nov 2008 20:41:48 PST

The logic of proofs (lp) was proposed as Gödel's missed link between Intuitionistic and S4-proofs, but so far the tableau-based methods proposed for lp have not explored this closeness with S4 and contain rules whose analycity is not immediately evident. We study possible formulations of analytic tableau proof methods for lp that preserve the subformula property. Two sound and complete tableau decision methods of increasing degree of analycity are proposed, KELP and preKELP. The latter is particularly inspired on S4-proofs. The crucial role of proof constants in the structure of lp-proofs methods is analysed. In particular, a method for the abduction of proof constant specifications in strongly analytic preKELP proofs is presented; abduction heuristics and the complexity of the method are discussed.

Finitely Presented MV-algebras with Finite Automorphism Group

Aguzzoli, S., Marra, V. — Fri, 14 Nov 2008 05:04:29 PST

We address the question, which MV-algebras have finite automorphism group. We prove that finitely presented MV-algebras whose maximal spectral space has topological dimension not exceeding 1 do have finite automorphism group. We give examples to show that finite presentability is an essential hypothesis. Our proof produces as an interesting by-product a complete graph–theoretic isomorphism invariant for the class of MV-algebras involved.

Bottom-up Construction of Semantic Tableaux

Peltier, N. — Thu, 13 Nov 2008 03:54:25 PST

We present a new proof procedure for first-order logic. Our approach is closely related to semantic tableaux, but it uses a more compact representation of the search space. The idea is to construct the tableau from the leaves to the root, which helps to factorize common subtrees and reduces the information that must be stored in a given branch. We prove that the method is sound and refutationally complete and we provide simplification rules in order to prune the search space and delete redundant inferences. We show that our procedure runs in polynomial time for several propositional classes, including the Horn-renamable class or the Krom class. This article is an extended version of Peltier (2007, LNAI 4548).

Model Checking Using Description Logic

Ben-David, S., Trefler, R., Weddell, G. — Thu, 13 Nov 2008 03:54:25 PST

Model checking is an automated technique for the verification of finite-state systems that is widely used in practice. In Bounded Model Checking (BMC) the system is checked only until a given execution depth from the initial state. State of the art model checkers apply Binary Decision Diagrams (BDDs) as well as Satisfiability Solving (SAT) for this task. However, both methods suffer from the state explosion problem, which restricts the application of model checking to only modestly sized systems. The importance of model checking makes it worthwhile to explore alternative technologies, in the hope of enabling the application of the technique to a wider class of systems. Description Logic (DL) is a family of knowledge representation formalisms, mainly used for designing ontologies, for which reasoning is based on tableaux techniques. In this article, we show how model checking problems can be solved using DL reasoning. We present two different encodings of a model checking problem as a consistency check in DL, and show how DL can serve as a natural setting for representing and solving a BMC problem. Experimental results, using the DL reasoner FaCT++, give encouraging results.

Axiom Pinpointing in General Tableaux

Baader, F., Penaloza, R. — Thu, 13 Nov 2008 04:21:14 PST

Axiom pinpointing has been introduced in description logics (DLs) to help the user to understand the reasons why consequences hold and to remove unwanted consequences by computing minimal (maximal) subsets of the knowledge base that have (do not have) the consequence in question. Most of the pinpointing algorithms described in the DLliterature are obtained as extensions of the standard tableau-based reasoning algorithms for computing consequences from DL knowledge bases. Although these extensions are based on similar ideas, they are all introduced for a particular tableau-based algorithm for a particular DL. The purpose of this article is to develop a general approach for extending a tableau-based algorithm to a pinpointing algorithm. This approach is based on a general definition of ‘tableau algorithms,’ which captures many of the known tableau-based algorithms employed in DLs, but also other kinds of reasoning procedures.

Call for Papers: Coalgebra & Logic

Mon, 26 Nov 2007 04:37:26 PST