Journal of Logic and Computation - recent issues

Natural Language and Knowledge Representation

Sukkarieh, J. Z. — 2008-05-15

Experience and History: Processes and their Relation to Events

Galton, A. — 2008-05-15

We develop a theory of processes which takes into account the observation that processes differ markedly from events in their relation to change. Whereas events are fixed items of history which cannot be described as undergoing change, processes are more like ordinary objects in that they can be directly present at one time and can undergo change as time proceeds. This leads to a fundamental ontological distinction between EXP, the dynamic experiential world of objects and processes as they exist at one time, and HIST, the static historical overview populated by events that are generated by the ongoing processes in EXP. Formally, this means that terms describing processes can serve as arguments to time-varying predicates, whereas terms describing events cannot. We illustrate this by presenting part of a suitable formalism and using it to give an account of the progressive aspect.

The Semantic Processing of Continuous Quantities for Discrete Terms in Ontologies

Wang, S., Rydeheard, D., Pan, J. Z. — 2008-05-15

We consider continuous quantities that are used to describe the physical world, such as colour, shape, sound, texture and spatial and temporal arrangements. Natural languages are not adept at describing these quantities, nor are they easily incorporated into ontologies in the form of discrete terms. In this article, we analyse the way that natural languages handle continuous quantities, propose a general semantics based on metric spaces, and describe how to treat semantic values computationally, so that we may automate the processing of texts which describe continuous quantities allowing, for example, query evaluation and the integration of multiple texts. This provides a basis for incorporating these quantities into ontologies and combining their semantics with automated reasoning tools. We run a series of experiments to evaluate the semantics, the general framework, and the computational system we have developed.

Extracting Frame-Semantics Knowledge using Lattice Theory

Valverde-Albacete, F. J. — 2008-05-15

In this article, we introduce a new representation based on lattice theory for lexical data from a lexical-database embodying the frame-semantic approach to language description, FrameNet. We present proof of the abundance of Concept Lattices as proposed in Formal Concept Analysis both in the theory of frames and in its present-day incarnation, the FrameNet resource, by constructing several types of these. We further argue for the adequacy of such lattices in representing linguistic data with contributions that range from data-visualization to the fine-tuning of some frame-theoretical concepts. We argue finally that FrameNet is better thought of as being a lexical resource rather than an ontology, but we make the case throughout the article for Concept Lattices being a linguistically adequate, formally effective intermediate representations from which knowledge representation languages may draw knowledge-rich, linguistic facts from FrameNet at their convenience.

Deverbal Nouns in Knowledge Representation

Gurevich, O., Crouch, R., King, T. H., de Paiva, V. — 2008-05-15

Deverbal nouns pose serious challenges for knowledge-representation systems. We present a method of canonicalizing deverbal noun representations, relying on a rich lexicon of verb subcategorization frames, the WordNet database, a large finite-state network for derivational morphology and a series of heuristics for mapping deverbal arguments onto the arguments of corresponding verbs.¹

Linking Semantic and Knowledge Representations in a Multi-Domain Dialogue System

Dzikovska, M. O., Allen, J. F., Swift, M. D. — 2008-05-15

We describe a two-layer architecture for supporting semantic interpretation and domain reasoning in dialogue systems. Building system that supports both semantic interpretation and domain reasoning in a transparent and well-integrated manner is an unresolved problem because of the diverging requirements of the semantic representations used in contextual interpretation versus the knowledge representations used in domain reasoning. We propose an architecture that provides both portability and efficiency in natural language interpretation by maintaining separate semantic and domain knowledge representations, and integrating them via an ontology mapping procedure. The ontology mapping is used to obtain representations of utterances in a form most suitable for domain reasoners and to automatically specialize the lexicon. The use of a linguistically motivated parser for producing semantic representations for complex natural language sentences facilitates building portable semantic interpretation components as well as connections with domain reasoners. Two evaluations demonstrate the effectiveness of our approach: we show that a small number of mapping rules are sufficient for customizing the generic semantic representation to a new domain, and that our automatic lexicon specialization technique improves parser speed and accuracy.

Speech Acts, Epistemic Planning and Grice's Maxims

Ramsay, A., Field, D. — 2008-05-15

Work on speech acts has generally involved the introduction of sets of different actions such as informing, reminding, bluffing and lying. These actions have different preconditions and effects, and hence can be used to achieve a wide variety of different real-world goals. The problem is that they tend to have indistinguishable surface forms. As such, it is extremely difficult for the hearer to decide which action she thinks has been performed, and it is therefore also extremely difficult for the speaker to be confident about how the hearer will respond. We will show how to achieve complex goals on the basis of a very simple set of linguistic actions. These actions have clearly marked surface forms, and hence can easily be distinguishable by a hearer. In order to do this, we have developed an epistemic planner with a number of interesting features, and with a number of optimisations that relate directly to aspects of the task at hand.

Testing the Reasoning for Question Answering Validation

Penas, A., Rodrigo, A., Sama, V., Verdejo, F. — 2008-05-15

Question answering (QA) is a task that deserves more collaboration between natural language processing (NLP) and knowledge representation (KR) communities, not only to introduce reasoning when looking for answers or making use of answer type taxonomies and encyclopaedic knowledge, but also, as discussed here, for answer validation (AV), that is to say, to decide whether the responses of a QA system are correct or not. This was one of the motivations for the first Answer Validation Exercise at CLEF 2006 (AVE 2006). The starting point for the AVE 2006 was the reformulation of the answer validation as a recognizing textual entailment (RTE) problem, under the assumption that a hypothesis can be automatically generated instantiating a hypothesis pattern with a QA system answer. The test collections that we developed in seven different languages at AVE 2006 are specially oriented to the development and evaluation of answer validation systems. We show in this article the methodology followed for developing these collections taking advantage of the human assessments already made in the evaluation of QA systems. We also propose an evaluation framework for AV linked to a QA evaluation track. We quantify and discuss the source of errors introduced by the reformulation of the answer validation problem in terms of textual entailment (around 2%, in the range of inter-annotator disagreement). We also show the evaluation results of the first answer validation exercise at CLEF 2006 where 11 groups have participated with 38 runs in seven different languages. The most extensively used techniques were Machine Learning and overlapping measures, but systems with broader knowledge resources and richer representation formalisms obtained the best results.

Utilizing Natural Language for One-Shot Task Learning

Jung, H., Allen, J., Galescu, L., Chambers, N., Swift, M., Taysom, W. — 2008-05-15

Learning tasks from a single demonstration presents a significant challenge because the observed sequence is specific to the current situation and is inherently an incomplete representation of the procedure. Observation-based machine-learning techniques are not effective without multiple examples. However, when a demonstration is accompanied by natural language explanation, the language provides a rich source of information about the relationships between the steps in the procedure and the decision-making processes that led to them. In this article, we present a one-shot task learning system built on TRIPS, a dialogue-based collaborative problem solving system, and show how natural language understanding can be used for effective one-shot task learning.

Lambda Calculus, Type Theory, and Natural Language II

Fox, C., Fernandez, M., Lappin, S. — 2008-03-13

Sequentially Indexed Grammars

van Eijck, J. — 2008-03-13

This article defines the grammar class of sequentially indexed grammars (SIGs) that results of a change in the index stack handling mechanism of indexed grammars (Aho, 1968, Journal of the ACM, 15, 647–671; 1969, Journal of the ACM, 16, 383–406). SIGs are different from linear indexed grammars (Gazdar, 1988, Natural Language, Parsing and Linguistic, Theories, pp. 69–94) (the rule format is simpler) and they generate a strictly larger language class. We give a polynomial algorithm for parsing with SIGs that is a rather straightforward extension of the Earley algorithm for parsing with context-free grammars. SIGs are attractive because of the simple rule format, the natural correspondence between indices and traces, and the perspicuity of the parsing scheme.

M. H. Newman's Typability Algorithm for Lambda-calculus

Hindley, J. R. — 2008-03-13

This article is essentially an extended review with historical comments. It looks at an algorithm published in 1943 by M. H. A. Newman, which decides whether a lambda-calculus term is typable without actually computing its principal type. Newman's algorithm seems to have been completely neglected by the type-theorists who invented their own rather different typability algorithms over 15 years later.

Proof Nets for Basic Discontinuous Lambek Calculus

Morrill, G., Fadda, M. — 2008-03-13

The theory of proof nets for continuity based on the Lambek calculus is well-developed, but we need a compatible extension to include discontinuity. Earlier work set out ingredients: hypersequent calculus and proof nets expanded with parameter edges. This article completes a preliminary line by finalizing a version of proof nets for the basic discontinuous Lambek calculus BDLC (the minimal system with one point of discontinuity) and proving correctness with respect to the hypersequent calculus.

Hyperintensions

Pollard, C. — 2008-03-13

Standard possible worlds semantics has been known from the start to have a problem with granularity: for a wide range of natural-language (NL) entailment patterns, not enough meaning distinctions are available to make predictions consistent with robust intuitions. Though numerous solutions have been proposed, often of great ingenuity and technical sophistication, none of these has gained widespread acceptance. As a result, most semanticists have made a practical decision to work in a framework known to have dubious foundations and leave the foundational problems to mathematical logicians. Here, a new approach is proposed which may be simple enough and conservative enough to be practical for working empirical and computational semanticists. More specifically, I show how the use of a higher-order logic with definable subtypes leads to a novel and surprisingly straightforward solution of the granularity problem. I also call attention to a hitherto unnoticed problem in standard approaches to NL semantics having to do with non-principal ultrafilters and show why it does not arise under my proposal. The two main technical innovations that drive the proposal are (i) axiomatizing NL entailment as a preorder (as opposed to an order) on the set of (primitive) propositions, and (ii) defining worlds as certain sets of propositions (viz. ultrafilters). These innovations provide just the tools we need to develop a formally explicit theory of hyperintensions, ¹ mathematical models of Fregean senses of a finer granularity than the familiar intensions (functions to extensions from worlds, where the worlds in turn are theoretical primitives) of mainstream Kripke/Montague-inspired NL semantics.

Computable Models

Turner, R. — 2008-03-13

We investigate mathematical modelling with theories of data types. We provide a formal setting for the formulation of such theories (TPL) and use it to introduce the notion of a computational model. We explore the notion and provide several case studies.

Introducing the Logic and Law Corner

Bench-Capon, T., Prakken, H. — 2008-01-21

In this article we introduce the Logic and Law corner of this journal. We will discuss a number of ways in which logic has been used in AI and Law, and give some of the key references to previous work on these topics. We will also list some important questions which we see as ready for further exploration. We encourage contributions on these, and other, Logic and Law issues.

Combining Syntax and Semantics through Prime Form Representation

Bittencourt, G. — 2008-01-21

This article presents an algorithm that, besides calculating the number of models of a propositional logic theory, also determines the distribution of these models among the terms of a disjunctive normal form representation of the theory. Using prime implicants to represent the target theory, in a knowledge compilation context, we discuss how this distribution can be used to define belief change operators that respect the theory structure. Some experimental results are also presented.

Analytic Calculi for Logics of Ordinal Multiples of Standard t-Norms

Vetterlein, T. — 2008-01-21

For two propositional fuzzy logics, we present analytic proof calculi, based on relational hypersequents. The logic considered first, called ML, is based on the finite ordinal sums of Lukasiewicz t-norms. In addition to the usual connectives—the conjunction , the implication -> and the constant 0—we use a further unary connective interpreted by the function associating with each truth value a the greatest -idempotent below a. ML is a conservative extension of Basic Logic.

The second logic, called M, is based on the finite ordinal sums of the product t-norm on (0, 1]. Our connectives are in this case just the conjunction and the implication.

A Presentation of Quantum Logic Based on an and then Connective

Lehmann, D. — 2008-01-21

When a physicist performs a quantic measurement, new information about the system at hand is gathered. This article studies the logical properties of how this new information is combined with previous information. It presents Quantum Logic as a propositional logic under two connectives: negation and the and then operation that combines old and new information. The and then connective is neither commutative nor associative. Many properties of this logic are exhibited, and some small elegant subset is shown to imply all the properties considered. No independence or completeness result is claimed. Classical physical systems are exactly characterized by the commutativity, the associativity, or the monotonicity of the and then connective. Entailment is defined in this logic and can be proved to be a partial order. In orthomodular lattices, the operation proposed by Finch in [3] satisfies all the properties studied in this article. All properties satisfied by Finch's; operation in modular lattices are valid in Quantum Logic. It is not known whether all properties of Quantum Logic are satisfied by Finch's; operation in modular lattices. Non-commutative, non-associative algebraic structures generalizing Boolean algebras are defined, ideals are characterized and a homomorphism theorem is proved.

On Variable-inactivity and Polynomial Formula-Satisfiability Procedures

Bonacina, M. P., Echenim, M. — 2008-01-21

Verification problems require to reason in theories of data structures and fragments of arithmetic. Thus, decision procedures for such theories are needed, to be embedded in, or interfaced with, proof assistants or software model checkers. Such decision procedures ought to be sound and complete, to avoid false negatives and false positives, efficient, to handle large problems, and easy to combine, because most problems involve multiple theories. The rewrite-based approach to decision procedures aims at addressing these sometimes conflicting issues in a uniform way, by harnessing the power of general first-order theorem proving. In this article, we generalize the rewrite-based approach from deciding the satisfiability of sets of ground literals to deciding that of arbitrary ground formulæ in the theory. Next, we present polynomial rewrite-based satisfiability procedures for the theories of records with extensionality and integer offsets. The generalization of the rewrite-based approach to arbitrary ground formulæ and the polynomial satisfiability procedure for the theory of records with extensionality use the same key property—termed variable-inactivity—that allows one to combine theories in a simple way in the rewrite-based approach.

Vector Logic: A Natural Algebraic Representation of the Fundamental Logical Gates

Mizraji, E. — 2008-01-21

Vector logic is a matrix–vector representation of the logical calculus inspired in neural network models. In this algebraic formalism, the truth values map on orthonormal Q-dimensional vectors, the monadic operations are represented by square matrices, and the dyadic operations produce rectangular matrices that act on the Kronecker product of the vector truth values. In this formalism, the theorems and tautologies of classical logic are demonstrated using the rules of matrix algebra. In the present work, we analyse a three-valued vector logic that adds to the ‘yes’ and ‘no’ vectors, a third ‘uncertain’ vector that represents the truth value corresponding to undecidable propositions. Fuzziness is produced both via linear combinations of ‘yes’ and ‘no’ vectors, and by the supplementary dimension of the logical vector subspace. We describe the basic matrix operators, and we show that for this three-valued vector logic, the modalities ‘possibility’ and ‘necessity’ are simple square matrices instead of infinite recursive processes. Finally, we explore the application of this formalism to represent the complex-valued operator$$\sqrt{\mathrm{NOT}}$$, and the usefulness of vector logic to understand the powers and limitations of some reversible logical computations.

Preservation of Interpolation Features by Fibring

Carnielli, W., Rasga, J., Sernadas, C. — 2008-01-21

Fibring is a metalogical constructor that permits to combine different logics by operating on their deductive systems under certain natural restrictions, as for example that the two given logics are presented by deductive systems of the same type. Under such circumstances, fibring will produce a new deductive system by means of the free use of inference rules from both deductive systems, provided the rules are schematic, in the sense of using variables that are open for application to formulas with new linguistic symbols (from the point of view of each logic component). Fibring is a generalization of fusion, a less general but wider developed mechanism which permits results of the following kind: if each logic component is decidable (or sound, or complete with respect to a certain semantics) then the resulting logic heirs such a property. The interest for such preservation results for combining logics is evident, and they have been achieved in the more general setting of fibring in several cases. The Craig interpolation property and the Maehara interpolation have a special significance when combining logics, being related to certain problems of complexity theory, some properties of model theory and to the usual (global) metatheorem of deduction. When the peculiarities of the distinction between local and global deduction interfere, justifying what we call careful reasoning, the question of preservation of interpolation becomes more subtle and other forms of interpolation can be distinguished. These questions are investigated and several (global and local) preservation results for interpolation are obtained for fibring logics that fulfill mild requirements.

Monotonic and Downward Closed Games

Abdulla, P. A., Bouajjani, A., D'orso, J. — 2008-01-21

In an earlier work [Abdulla et al. (2000, Information and Computation, 160, 109–127)] we presented a general framework for verification of infinite-state transition systems, where the transition relation is monotonic with respect to a well quasi-ordering on the set of states. In this article, we investigate extending the framework from the context of transition systems to that of games with infinite state spaces. We show that monotonic games with safety winning conditions are in general undecidable. In particular, we show this negative results for games which are defined over Petri nets. We identify a subclass of monotonic games, called downward closed games. We provide algorithms for analysing downward closed games subject to safety winning conditions. We apply the algorithm to games played on lossy channel systems. Finally, we show that weak parity games are undecidable for the above classes of games.

Cut Elimination and Decidability for Classical Lambek Logic

Ilic, M. I. — 2008-01-21

In this article we give a cut elimination procedure for two-sided sequent system of classical Lambek logic and, on the basis of the presented procedure, a new proof of decidability for this logic.

Call for Papers

2008-01-21