Journal of Logic and Computation - Advance Access

On the Density of Truth of Locally Finite Logics

Kostrzycka, Z. — 2009-06-26

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. — 2009-06-26

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. — 2009-06-26

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. — 2009-06-26

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. — 2009-06-16

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. — 2009-06-16

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. — 2009-05-04

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. — 2009-05-04

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. — 2009-05-04

A Graph-theoretic Account of Logics

Sernadas, A., Sernadas, C., Rasga, J., Coniglio, M. — 2009-04-22

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. — 2009-03-26

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. — 2009-03-26

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. — 2009-03-26

The Logic of Acceptance: Grounding Institutions on Agents' Attitudes

Lorini, E., Longin, D., Gaudou, B., Herzig, A. — 2009-03-26

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. — 2009-03-18

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. — 2009-03-18

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. — 2009-03-18

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. — 2009-03-13

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. — 2009-03-13

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. — 2009-03-13

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. — 2009-03-12

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. — 2009-03-10

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. — 2009-03-10

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. — 2009-03-05

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. — 2009-02-27

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. — 2009-02-26

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. — 2009-02-20

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. — 2009-02-17

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. — 2009-02-12

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. — 2009-02-12

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. — 2009-02-09

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. — 2009-02-03

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. — 2009-01-22

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

Alberucci, L. — 2009-01-22

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. — 2009-01-20

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. — 2009-01-08

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. — 2009-01-08

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. — 2008-12-23

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. — 2008-12-22

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. — 2008-12-22

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. — 2008-12-22

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. — 2008-12-22

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. — 2008-12-17

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. — 2008-12-12

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. — 2008-12-12

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. — 2008-12-06

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. — 2008-12-05

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. — 2008-11-27

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. — 2008-11-27

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. — 2008-11-26

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. — 2008-11-26

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. — 2008-11-21

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. — 2008-11-21

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. — 2008-11-20

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. — 2008-11-20

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. — 2008-11-17

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. — 2008-11-17

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. — 2008-11-17

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. — 2008-11-16

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. — 2008-11-16

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. — 2008-11-16

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. — 2008-11-14

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. — 2008-11-13

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. — 2008-11-13

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. — 2008-11-13

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.

A Multi-Agent System for Dynamic Ontologies

Ottens, K., Hernandez, N., Gleizes, M.-P., Aussenac-Gilles, N. — 2008-10-22

In the article, we present Dynamo (an acronym of DYNAMic Ontologies), a tool based on an adaptive multi-agent system to construct and maintain an ontology from a domain-specific set of texts. The originality of our proposal is that the adaptative multi-agent system is used both to represent the ontology itself and to produce the ontology. This enables us to propose a system building and maintaining dynamically an ontology according to interactions with the user (also called the ontologist). We present our system and the mechanisms used to build and maintain the ontology from the texts and for the interactions with the ontologist. We also give results of the evaluation of our system.

Multimedia Interpretation for Dynamic Ontology Evolution

2008-09-30

The recent success of distributed and dynamic infrastructures for knowledge sharing has raised the need for semiautomatic/automatic ontology evolution strategies. Ontology evolution is generally defined as the timely adaptation of an ontology to changing requirements and the consistent propagation of changes to dependent artifacts. In this article, we present an ontology evolution approach in the context of multimedia interpretation. Ontology evolution in this context relies on the results obtained through reasoning for the interpretation of multimedia resources, through population of the ontology with new individuals or through enrichment of the ontology with new concepts and new semantic relations. The article analyses the results of interpretation, population and enrichment obtained in evaluation experiments in terms of measures such as precision and recall. The evaluation reveals encouraging results.

Trust-based Revision for Expressive Web Syndication

Golbeck, J., Halaschek-Wiener, C. — 2008-09-30

Interest in web-based syndication systems has been growing as information streams onto the web at an increasing rate. Technologies, like the standard Semantic Web languages RDF and OWL, make it possible to create expressive representations of the content of publications and subscriptions in a syndication framework. Because these languages are based in description logics, this representation allows the application to reasoning to make more precise matching of user interests with published information. A challenge to this approach is that the consistency of the underlying knowledge base must be maintained for these techniques to work. With the frequent addition of information from new publications, it is likely that inconsistencies will arise. There are many potential mechanisms for choosing which inconsistent information to discard from the KB to regain consistency; in the case of news syndication, we argue keeping the most trusted information is important for generating the most valuable matches. Thus, in this article, we present algorithms for belief-base revision, and specifically look at the user's trust in the information sources as a metric for deciding what to keep in the KB and what to remove.

Base Revision for Ontology Debugging

Ribeiro, M. M., Wassermann, R. — 2008-09-05

Belief Revision deals with the problem of adding new information to a knowledge base in a consistent way. Ontology Debugging, on the other hand, aims to find the axioms in a terminological knowledge base which caused the base to become inconsistent. In this article, we propose a belief revision approach in order to find and repair inconsistencies in ontologies represented in some description logic (DL). As the usual belief revision operators cannot be directly applied to DLs, we propose new operators that can be used with more general logics and show that, in particular, they can be applied to the logics underlying OWL-DL and Lite.

The Significance of Memory Costs in Answer Set Solver Implementation

Brain, M., De Vos, M. — 2008-09-05

Implementation costs linked to processor memory subsystems (cache miss costs, stalls due to bandwidth limits, etc.) have been shown to be a factor in the performance of a variety of declarative programming tools. This article investigates their impact on answer set solvers and the factors that control them. Experiments independently altering the size and difficulty of input programs allow a qualitative assessment of whether input program or solver design is a greater factor and a quantitative assessment of how much of problem these issues create.Avariety of processor performance metrics are recorded and used to provide a detailed picture of what limits solver performance and dispel a number of common misapprehensions.To demonstrate the degree to which these problems can be addressed, smodels-ie is presented. This is a version of the smodels solver with a number of implementation changes to improve cache utilisation, one major aspect of memory costs.

Category-based Equational Reasoning: An Approach to Ontology Integration

Geldart, J., Song, W. — 2008-08-22

Incorporating dynamic, general computational knowledge into Semantic Web ontologies is becoming increasingly important. The Semantic Web is now being used to model the behaviour of highly dynamic domains such as web-services, but current approaches to ontologies [such as Web Ontology Language (OWL)] are static and crisp. This article develops a new semantics for Resource Description Framework (RDF) based upon ideas from category theory. In so doing, we not only decouple RDF's semantics from crisp set theory, opening the door to easy adoption of models of uncertainty, but also allow the use of equational reasoning in a principled fashion within RDF. We demonstrate the abilities of equational reasoning, whilst explaining its semantic principles in terms of our RDF category, using an example from the domain of genealogy. We further develop an algebra of (equational) ontologies which allows us to express fine relations between ontologies and to build more complex ontologies out of simpler ones.

Monotonic Answer Set Programming

Gebser, M., Gharib, M., Mercer, R., Schaub, T. — 2008-08-22

Answer set programming (ASP) does not allow for incrementally constructing answer sets or locally validating constructions like proofs by only looking at a part of the given program. In this article, we elaborate upon an alternative approach to ASP that allows for incremental constructions. Our approach draws its basic intuitions from the area of default logics. We investigate the feasibility of the concept of semi-monotonicity known from default logics as a basis of incrementality. On the one hand, every logic program has at least one answer set in our alternative setting, which moreover can be constructed incrementally based on generating rules. On the other hand, the approach may produce answer sets lacking characteristic properties of standard answer sets, such as being a model of the given program. We show how integrity constraints can be used to re-establish such properties, even up to correspondence with standard answer sets. Furthermore, we develop an SLD-like proof procedure for our incremental approach to ASP, which allows for query-oriented computations. Also, we provide a characterization of our definition of answer sets via a modification of Clark's completion. Based on this notion of program completion, we present an algorithm for computing the answer sets of a logic program in our approach.

Efficiently Querying RDF(S) Ontologies with Answer Set Programming

Ianni, G., Martello, A., Panetta, C., Terracina, G. — 2008-08-21

Ontologies are pervading many areas of knowledge representation and management. To date, most research efforts have been spent on the development of sufficiently expressive languages for the representation and querying of ontologies; however, querying efficiency has received attention only recently, especially for ontologies referring to large amounts of data. In fact, it is still uncertain how reasoning tasks will scale when applied on massive amounts of data. This work is a first step toward this setting: it first shows that Resource Description Framework(Schema) [RDF(S)] ontologies can be expressed, without loss of semantics, into Answer Set Programming (ASP). Then, based on a previous result showing that the SPARQL query language (a candidate W3C recommendation for RDF(S) ontologies) can be mapped to a rule-based language, it shows that efficient querying of big ontologies can be accomplished with a database oriented extension of the well known ASP system DLV, which we recently developed. Results reported in the article show that our proposed framework is promising for the improvement of both scalability and expressiveness of available RDF(S) storage and query systems.

Reasoning Support for Mapping Revision

Meilicke, C., Stuckenschmidt, H., Tamilin, A. — 2008-08-14

Finding correct semantic correspondences between heterogeneous ontologies is one of the most challenging problems in the area of semantic web technologies. As manually constructing such mappings is not feasible in realistic scenarios, a number of automatic matching tools have been developed that propose mappings based on general heuristics. As these heuristics often produce incorrect results, a manual revision is inevitable in order to guarantee the quality of generated mappings. Experiences with benchmarking matching systems revealed that the manual revision of mappings is still a very difficult problem because it has to take the semantics of the ontologies as well as interactions between mappings into account. In this article, we propose methods for supporting human experts in the task of revising automatically created mappings. In particular, we present non-standard reasoning methods for detecting and propagating implications of expert decisions on the correctness of a mapping.

OntoDLV: An ASP-based System for Enterprise Ontologies

Ricca, F., Gallucci, L., Schindlauer, R., Dell'armi, T., Grasso, G., Leone, N. — 2008-08-14

Enterprise/Corporate ontologies are widely adopted to conceptualize business enterprise information. In this area, the semantic peculiarities ofAnswer Set Programming (ASP), like the ClosedWorld Assumption (CWA) and the Unique NameAssumption (UNA), are more appropriate than the OntologyWeb Language (OWL) assumptions, also because such ontologies frequently stem from relational databases, where both CWA and UNA are adopted. This article presents OntoDLV, a system based on ASP for the specification and reasoning on enterprise ontologies. OntoDLV implements a powerful ontology representation language, called OntoDLP, extending (disjunctive) ASP with all the main ontology features including classes, inheritance, relations and axioms. OntoDLP is strongly typed, and includes also complex type constructors, like lists and sets. Importantly, OntoDLV supports a powerful interoperability mechanism with OWL, allowing the user to retrieve information from OWL ontologies, and build rule-based reasoning on top of OWL ontologies. The system is already used in a number of real-world applications including agent-based systems, information extraction, and text classification.

A Translation-based Approach to the Verification of Modular Equivalence

Oikarinen, E., Janhunen, T. — 2008-08-09

The goal of this article is to foster modular program development in answer set programming using a Gaifman-Shapiro-style module architecture. More specifically, a method for verifying the equivalence of logic program modules is devised and proved correct. The idea is to adapt a translation-based verification technique, which was originally devised for complete programs only, for program modules. In addition, optimization strategies are addressed in order to exploit the modular structure of programs in verification tasks. A number of experiments on verification strategies are also conducted using lpeq which implements the verification method for the smodels system. The preliminary experimental results reported in this article suggest that the modularization of equivalence verification leads to potential time savings especially if the modules involved share a common context.

On Instance-level Update and Erasure in Description Logic Ontologies

De Giacomo, G., Lenzerini, M., Poggi, A., Rosati, R. — 2008-08-06

A Description Logic (DL) ontology is constituted by two components, a TBox that expresses general knowledge about the concepts and their relationships, and an ABox that describes the properties of individuals that are instances of concepts. We address the problem of how to deal with changes to a DL ontology, when these changes affect only the ABox, i.e. when the TBox is considered invariant. We consider two basic changes, namely instance-level update and instance-level erasure, roughly corresponding to the addition and the deletion of a set of facts involving individuals. We characterize the semantics of instance-level update and erasure on the basis of the approaches proposed by Winslett and by Katsuno and Mendelzon. Interestingly, DLs are typically not closed with respect to instance-level update and erasure, in the sense that the set of models corresponding to the application of any of these operations to a knowledge base in a DL $$\mathcal{L}$$ may not be expressible by ABoxes in $$\mathcal{L}$$. In particular, we show that this is true for DL-Lite$$\mathcal{F}$$, a tractable DL that is oriented towards data-intensive applications. To deal with this problem, we first introduce DL-Lite$$\mathcal{FS}$$, a DL that minimally extends DL-Lite$$\mathcal{F}$$ and is closed with respect to instance-level update, and present a polynomial algorithm for computing instance-level update in this logic. Then, we provide a principled notion of best approximation with respect to a fixed language $$\mathcal{L}$$ of instance-level update and erasure, and exploit the algorithm for instance-level update for DL-Lite$$\mathcal{FS}$$ to get polynomial algorithms for approximated instance-level update and erasure for DL-Lite$$\mathcal{F}$$. These results confirm the nice computational properties of DL-Lite$$\mathcal{F}$$ for data intensive applications, even where information about instances is not only read, but also written.

From (Quantified) Boolean Formulae to Answer Set Programming

Stephan, I., Da Mota, B., Nicolas, P. — 2008-08-06

We propose in this article a translation from quantified Boolean formulae to answer set programming. The computation of a solution of a quantified Boolean formula is then equivalent to the computation of a stable model for a normal logic program. The case of unquantified Boolean formulae is also considered since it is equivalent to the case of quantified Boolean formulae with only existential quantifiers.

Experimental Analysis of Graph-based Answer Set Computation over Parallel and Distributed Architectures

Grossi, G., Marchi, M., Pontelli, E., Provetti, A. — 2008-08-05

This article presents a distributed version of the adjSolver algorithm for computing the answer sets of logic programs. adjSolver operates a classical branch-and-bound structure; its intrinsic parallelism is exploited to control, with a centralized architecture, the delegation of promising search subspaces to distributed handling agents. adjSolver has been implemented and tested on a Beowulf platform, using MPI message passing. The communication overhead was minimized by adopting a compact representation of the data exchanged among agents and by reusing previously-computed partial solutions.

Call for Papers: Coalgebra & Logic

2007-11-26