Showing papers in "Journal of Logic, Language and Information in 2002"

Games That Agents Play: A Formal Framework for Dialogues between Autonomous Agents

Abstract: We present a logic-based formalism for modeling of dialogues between intelligent and autonomous software agents, building on a theory of abstract dialogue games which we present. The formalism enables representation of complex dialogues as sequences of moves in a combination of dialogue games, and allows dialogues to be embedded inside one another. The formalism is computational and its modular nature enables different types of dialogues to be represented.

Extensive Games as Process Models

Abstract: We analyze extensive games as interactive process models, using modal languages plus matching notions of bisimulation as varieties of game equivalences. Our technical results show how to fit existing modal notions into this new setting.

Some Notes on the Formal Properties of Bidirectional Optimality Theory

Abstract: In this paper, we discuss some formal properties of the model of bidirectional Optimality Theory that was developed in Blutner (2000). We investigate the conditions under which bidirectional optimization is a well-defined notion, and we give a conceptually simpler reformulation of Blutner's definition. In the second part of the paper, we show that bidirectional optimization can be modeled by means of finite state techniques. There we rely heavily on the related work of Frank and Satta (1998) about unidirectional optimization.

Descriptions of Game Actions

Abstract: To describe simultaneous knowledge updates for different subgroups we propose an epistemic language with dynamic operators for actions. The language is interpreted on equivalence states (S5 states). The actions are interpreted as state transformers. Two crucial action constructors are learning and local choice. Learning is the dynamic equivalent of common knowledge. Local choice aids in constraining the interpretation of an action to a functional interpretation (state transformer). Bisimilarity is preserved under execution of actions. The language is applied to describe various actions in card games.

Compositional Verification of Multi-Agent Systems in Temporal Multi-Epistemic Logic

Abstract: Compositional verification aims at managing the complexity of the verification process by exploiting compositionality of the system architecture. In this paper we explore the use of a temporal epistemic logic to formalize the process of verification of compositional multi-agent systems. The specification of a system, its properties and their proofs are of a compositional nature, and are formalized within a compositional temporal logic: Temporal Multi-Epistemic Logic. It is shown that compositional proofs are valid under certain conditions. Moreover, the possibility of incorporating default persistence of information in a system, is explored. A completion operation on a specific type of temporal theories, temporal completion, is introduced to be able to use classical proof techniques in verification with respect to non-classical semantics covering default persistence.

Meaning and Use of Indefinite Expressions

Abstract: Sentences containing pronouns and indefinite noun phrases can be said to express open propositions, propositions which display gaps to be filled. This paper addresses the question what is the linguistic content of these expressions, what information they can be said to provide to a hearer, and in what sense the information of a speaker can be said to support their utterance. We present and motivate first order notions of content, update and support. The three notions are each defined in a compositional fashion and brought together within a single and coherent framework.

Independent Choices and the Interpretation of IF Logic

Abstract: In this paper it is argued that Hintikka's game theoretical semantics for Independence Friendly logic does not formalize the intuitions about independent choices; it rather is a formalization of imperfect information. Furthermore it is shown that the logic has several remarkable properties (e.g., renaming of bound variables is not allowed). An alternative semantics is proposed which formalizes intuitions about independence.

A Two-Variable Fragment of English

Abstract: Controlled languages are regimented fragments of natural language designed to make the processing of natural language more efficient and reliable. This paper defines a controlled language, E2V, whose principal grammatical resources include determiners, relative clauses, reflexives and pronouns. We provide a formal syntax and semantics for E2V, in which anaphoric ambiguities are resolved in a linguistically natural way. We show that the expressive power of E2V is equal to that of the two-variable fragment of first-order logic. It follows that the problem of determining the satisfiability of a set of E2V sentences is NEXPTIME complete. We show that E2V can be extended in various ways without compromising these complexity results; however, relaxing our policy on anaphora resolution renders the satisfiability problem for E2V undecidable. Finally, we argue that our results have a bearing on the broader philosophical issue of the relationship between natural and formal languages.

ML Systems: A Proof Theory for Contexts

Abstract: In the last decade the concept of context has been extensively exploited in many research areas, e.g., distributed artificial intelligence, multi agent systems, distributed databases, information integration, cognitive science, and epistemology. Three alternative approaches to the formalization of the notion of context have been proposed: Giunchiglia and Serafini's Multi Language Systems (ML systems), McCarthy's modal logics of contexts, and Gabbay's Labelled Deductive Systems. Previous papers have argued in favor of ML systems with respect to the other approaches. Our aim in this paper is to support these arguments from a theoretical perspective. We provide a very general definition of ML systems, which covers all the ML systems used in the literature, and we develop a proof theory for an important subclass of them: the MR systems. We prove various important results; among other things, we prove a normal form theorem, the sub-formula property, and the decidability of an important instance of the class of the MR systems. The paper concludes with a detailed comparison among the alternative approaches.

Substructural Logics with Mingle

Abstract: We introduce structural rules mingle, and investigate theorem-equivalence, cut- eliminability, decidability, interpolability and variable sharing property for sequent calculi having the mingle. These results include new cut-elimination results for the extended logics: FLm (full Lambek logic with the mingle), GLm (Girard's linear logic with the mingle) and Lm (Lambek calculus with restricted mingle).

Kripke Semantics for Modal Substructural Logics

Abstract: We introduce Kripke semantics for modal substructural logics, and prove the completeness theorems with respect to the semantics. The completeness theorems are proved using an extended Ishihara's method of canonical model construction (Ishihara, 2000). The framework presented can deal with a broad range of modal substructural logics, including a fragment of modal intuitionistic linear logic, and modal versions of Corsi's logics, Visser's logic, Mendez's logics and relevant logics.

Naming Worlds in Modal and Temporal Logic

Abstract: In this paper we suggest adding to predicate modal and temporal logic a locality predicate W which gives names to worlds (or time points). We also study an equal time predicate D(x, y) which states that two time points are at the same distance from the root. We provide the systems studied with complete axiomatizations and illustrate the expressive power gained for modal logic by simulating other logics. The completeness proofs rely on the fairly intuitive notion of a configuration in order to use a proof technique similar to a Henkin completion mixed with a tableau construction. The main elements of the completeness proofs are given for each case, while purely technical results are grouped in the appendix.

Bayesianism and Language Change

Abstract: Bayesian probability is normally defined over a fixed language or event space. But in practice language is susceptible to change, and the question naturally arises as to how Bayesian degrees of belief should change as language changes. I argue here that this question poses a serious challenge to Bayesianism. The Bayesian may be able to meet this challenge however, and I outline a practical method for changing degrees of belief over changes in finite propositional languages.

Spanish Inflectional Morphology in DATR

Abstract: This paper shows a full description of Spanish inflectional morphology. We have chosen a paradigmatic approach instead of one based on phonological/spelling changes, i.e., the typical two-level model. Such morphological description has been written in the DATR formalism. The result is a network of nodes that makes use of the information inheritance mechanisms – orthogonal node inheritance and default path inheritance – that DATR allows. Some lexical coverage and corpus occurrence figures that support our approach are also given.

The Donkey and the Monoid.Dynamic Semantics with Control Elements

Abstract: Dynamic Predicate Logic (DPL) is a variant of Predicate Logic introduced by Groenendijk and Stokhof. One rationale behind the introduction of DPL is that it is closer to Natural Language than ordinary Predicate Logic in the way it treats scope. In this paper I develop some variants of DPL that can more easily approximate Natural Language in some further aspects. Specifically I add flexibility in the treatment of polarity and and some further flexibility in the treatment of scope. I develop a framework that is intended to encourage further experimentation with alternative variants of DPL. In this framework the new meanings are, roughly, indexed sets of old meanings. The indices can be viewed as "files'' or "storage devices.'' Each such file supports a separate "information stream.'' The interaction of the new meanings is "programmed'' with the help of certain monoids acting on the indices. The construction of the new meanings can be viewed as an application of the Grothendieck Construction to monoids.

Coordination in an Email Game without ``Almost Common Knowledge''

Abstract: The paper presents a variation of the EMAIL Game, originally proposed by Rubinstein (American Economic Review, 1989), in which coordination of the more rewarding-risky joint course of actions is shown to obtain, even when the relevant game is, at most, ``mutual knowledge.'' In the example proposed, a mediator is introduced in such a way that two individuals are symmetrically informed, rather than asymmetrically as in Rubinstein, about the game chosen by nature. As long as the message failure probability is sufficiently low, with the upper bound being a function of the game payoffs, conditional beliefs in the opponent's actions can allow players to choose a more rewarding-risky action. The result suggests that, for efficient coordination to obtain, the length of interactive knowledge on the game, possibly up to ``almost common knowledge,'' does not seem to be a major conceptual issue and that emphasis should be focused instead on the communication protocol and an appropriate relationship between the reliability of communication channels and the payoffs at stake.

Entrenchment versus Dependence: Coherence and Foundations in Belief Change

Abstract: We describe the relation between coherence and foundations approaches to belief change in terms of a correspondence between epistemic entrenchment relations (Gardenfors and Makinson, 1988; Rott, 1992) and dependence consequence relations from Bochman (1999, 2000a) The general conclusion of the study is that dependence consequence relations are sufficiently expressive to subsume the notion of an epistemic entrenchment and its generalizations

Referent Systems and Relational Grammar

Abstract: Relational Grammar (RG) was introduced in the 1970s as a theory of grammatical relations and relation change, for example, passivization, dative shift, and raising Furthermore, the idea behind RG was that transformations as originally designed in generative grammar were unable to capture the common kernel of, eg, passivization across languages The research conducted within RG has uncovered a wealth of phenomena for which it could produce a satisfactory analysis Although the theory of Government and Binding has answered some of the complaints, still it left many phenomena unaccounted for Referent Systems (RSs) have been introduced by Vermeulen (1995) to overcome certain weaknesses of Dynamic Semantics Their usefulness has not yet been realized in semantical theory We shall show here that their significance cannot be overestimated Namely, we will show in this paper that there exists a fundamental affinity to RG Both handle the relation between an argument and a functor by means of a shared relational sign, which is unique for each argument This assignment can be changed What is interesting is that the notion of a chomeur, which is central to RG, finds a natural treatment in RSs This coincidence is in our view not accidental but reveals some fundamental properties of the human language faculty

Linear, Branching Time and Joint ClosureSemantics for Temporal Logic

Abstract: Temporal logic can be used to describe processes: their behaviour is characterized by a set of temporal models axiomatized by a temporal theory. Two types of models are most often used for this purpose: linear and branching time models. In this paper a third approach, based on socalled joint closure models, is studied using models which incorporate all possible behaviour in one model. Relations between this approach and the other two are studied. In order to define constructions needed to relate branching time models, appropriate algebraic notions are defined (in a category theoretical manner) and exploited. In particular, the notion of joint closure is used to construct one model subsuming a set of models. Using this universal algebraic construction we show that a set of linear models can be merged to a unique branching time model. Logical properties of the described algebraic constructions are studied. The proposed approach has been successfully aplied to obtain an appropriate semantics for non-monotonic reasoning processes based on default logic. References are discussed that show the details of these applications.

One Connection between Standard Invariance Conditions on ModalFormulas and Generalized Quantifiers

Abstract: The language of standard propositional modal logic has one operator (s or ♦), that can be thought of as being determined by the quantifiers ∀ or ∃, respectively: for example, a formula of the form sφ is true at a point s just in case all the immediate successors of s verify φ. This paper uses a propositional modal language with one operator determined by a generalized quantifier to discuss a simple connection between standard invariance conditions on modal formulas and generalized quantifiers: the combined generalized quantifier conditions of conservativity and extension correspond to the modal condition of invariance under generated submodels, and the modal condition of invariance under bisimulations corresponds to the generalized quantifier being a Boolean combination of ∀ and ∃.

A Tableau Method for Graded Intersections of Modalities: A Case for Concept Languages

Abstract: A concept language with role intersection and number restriction is defined and its modal equivalent is provided. The main reasoning tasks of satisfiability and subsumption checking are formulated in terms of modal logic and an algorithm for their solution is provided. An axiomatization for a restricted graded modal language with intersection of modalities (the modal counterpart of the concept language we examine) is given and used in the proposed algorithm.

Elementary Definability and Completeness in General and Positive Modal Logic

Abstract: The paper generalises Goldblatt's completeness proof for Lemmon–Scott formulas to various modal propositional logics without classical negation and without ex falso, up to positive modal logic, where conjunction and disjunction, and where necessity and possibility are respectively independent. Further the paper proves definability theorems for Lemmon–Scott formulas, which hold even in modal propositional languages without negation and without falsum. Both, the completeness theorem and the definability theorem make use only of special constructions of relations, like relation products. No second order logic, no general frames are involved.

A Syntactic Framework with Probabilistic Beliefs and Conditionals for the Analysis of Strategic Form Games

Abstract: In this paper, I develop a syntactic framework for the analysis of strategic form games that is based on a straightforward combination of standard systems of doxastic, probabilistic and conditional propositional logic In particular, for the probabilistic part I make use of the axiomatization provided in Fagin and Halpern (1994) The use of conditionals allows to represent a strategic form game by a logical formula in a very natural way Also expected utility maximization can be naturally captured I use this framework to prove a version of a result on Nash equilibrium conjectures first presented in Aumann and Brandenburger (1995)