Showing papers in "Journal of Logic and Computation in 1998"

Agents that Reason and Negotiate by Arguing

Abstract: The need for negotiation in multi-agent systems stems from the requirement for agents to solve the problems posed by their interdependence upon one another. Negotiation provides a solution to these problems by giving the agents the means to resolve their conflicting objectives, correct inconsistencies in their knowledge of other agents' world views, and coordinate a joint approach to domain tasks which benefits all the agents concerned. We propose a framework, based upon a system of argumentation, which permits agents to negotiate in order to establish acceptable ways of solving problems. The framework provides a formal model of argumentation-based reasoning and negotiation, details a design philosophy which ensures a clear link between the formal model and its practical instantiation, and describes a case study of this relationship for a particular class of architectures (namely those for belief-desire-intention agents).

Decision Procedures for BDI Logics

Abstract: The study of computational agents capable of rational behaviour has received increasing attention in recent years. A number of theoretical formalizations for such multi-agent systems have been proposed. However, most of these formalizations do not have a strong semantic basis nor a sound and complete axiomatization. Hence, it has not been clear as to how these formalizations could assist in building agents in practice. This paper explores a particular type of multi-agent system, in which each agent is viewed as having the three mental attitudes of belief (B), desire (D), and intention (I). It provides a family of multi-modal branching-time BDI logics with a possible-worlds semantics, categorizes them, provides sound and complete axiomatizations, and gives constructive tableau-based decision procedures for testing the satisfiability and validity of formulas. The computational complexity of these decision procedures is no greater than the complexity of their underlying temporal logic component.

Engineering AgentSpeak(L): A Formal Computational Model

Abstract: Perhaps the most successful agent architectures, and certainly the best known, are those based on the Belief-Desire-Intention (BDI) framework. Despite the wealth of research that has accumulated on both formal and practical aspects of this framework, however, there remains a gap between the formal models and the implemented systems. In this paper, we build on earlier work by Rao aimed at narrowing this gap, by developing a strongly-typed, formal, yet computational model of the BDI-based AgentSpeak(L) language. AgentSpeak(L) is a programming language, based on the Procedural Reasoning System (PRS) and the Distributed Multi-Agent Reasoning System (dMARS), which determines the behaviour of the agents it implements. In developing the model, we add to Rao's work, identify some omissions, and progress beyond the description of a particular language by giving a formal specification of a general BDI architecture that can be used as the basis for providing further formal specifications of more sophisticated systems.

Resolution for temporal logics of knowledge

Abstract: A resolution based proof system for a temporal logic of knowledge is p re ented and shown to be correct. Such logics are useful for proving properties of distribut ed and multi-agent systems. Examples are given to illustrate the proof system. An extension of th e basic system to the multimodal case is given and illustrated using the ‘muddy children problem’.

Actions Speak Louder than Words: Proving Bisimilarity for Context-Free Processes

Abstract: J.C.M. Baeten et al. (Lecture Notes in Computer Science, vol. 259, pp. 93-114, 1987) proved that bisimulation equivalence is decidable for irredundant context-free grammars. A much simpler and much more direct proof of this result is provided now. It uses a tableau decision method involving goal-directed rules. The decision procedure yields an upper bound on a tableau depth. Moreover, it provides the essential part of the bisimulation relation between two processes which underlies their equivalence. A second virtue is that it provides a sound and complete equational theory for such processes. >

Abductive Analysis of Modular Logic Programs

Abstract: We introduce a practical method for abductive analysis of modular logic programs. This is obtained by reversing the deduction process, which is usually applied in static-dataflow analysis of logic programs, on generic, possibly abstract, domains for analysis. The approach is validated in the framework of abstract interpretation. The abduced information provides an abstract specification for program modules which can be of assistance both in top-down development of programs and in compile-time optimization. To the best of our knowledge this is the first application of abductive reasoning in dataflow analysis of logic programs.

On the Decidability of Continuous Time Specification Formalisms

Abstract: We consider an interpretation of monadic second-order logic of order in the continuous time structure of finitely variable signals and show the decidability of monadic logic in this structure. The expressive power of monadic logic is illustrated by providing a straightforward meaning preserving translation into monadic logic of three typical continuous time specification formalism: temporal logic of reals, restricted duration calculus and the propositional fragment of mean value calculus. As a by-product of the decidability of monadic logic we obtain that the above formalisms are decidable even when extended by quantifiers.

A Modal Extension of Logic Programming: Modularity, Beliefs and Hypothetical Reasoning

Abstract: In this paper we present a modal extension of logic programming, which allows both multiple modalities and embedded implications. We show that this extension is well suited for structuring knowledge and, speci cally, for de ning module constructs within programs, for representing agents beliefs, and also for hypothetical reasoning. The language contains modalities [ai] to represent agent beliefs, and a modality 2 which is a kind of common knowledge operator. It allows sequences of modalities to occur in front of clauses, goals and clause heads, and hypothetical implications to occur in goals and in clause bodies. A goal directed proof procedure of the language is presented, and several examples of its use for de ning modules are given. In particular, the language is shown to capture di erent proposal for module de nition and composition presented in the literature. The modal logic, of which our programming language is a clausal fragment, is introduced through its Kripke semantics. This semantics has strong similarities with the possible world semantics for the (propositional) logics of knowledge and belief proposed by Halpern and Moses, though the modality 2 is weaker than common knowledge operator. A cut free sequent calculus is also given for this logic, and it is used to prove soundness and completeness of the goal directed proof procedure on the clausal fragment. In particular, goal directed proofs are shown to correspond to sequent proofs of a certain kind.

Occurrences and Narratives as Constraints in the Branching Structure of the Situation Calculus

Abstract: The Situation Calculus is a logic of time and change in which there is a distinguished initial situation and all other situations arise from the different sequences of actions that might be performed starting in the initial one. Within this framework, it is difficult to incorporate the notion of an occurrence, since all situations after the initial one are hypothetical. These occurrences are important, for instance, when one wants to represent narratives. There have been proposals to incorporate the notion of an action occurrence in the language of the Situation Calculus, namely Miller and Shanahan’s work on narratives [22] and Pinto and Reiter’s work on actual lines of situations [27, 29]. Both approaches have in common the idea of incorporating a linear sequence of situations into the tree described by theories written in the Situation Calculus language. Unfortunately, several advantages of the Situation Calculus are lost when reasoning with a narrative line or with an actual line of occurrences. In this paper we propose a different approach to dealing with action occurrences and narratives, which can be seen as a generalization of narrative lines to narrative trees. In this approach we exploit the fact that, in the discrete Situation Calculus [13], each situation has a unique history. Then, occurrences are interpreted as constraints on valid histories. We argue that this new approach subsumes the linear approaches of Miller and Shanahan’s, and Pinto and Reiter’s. In this framework, we are able to represent various kinds of occurrences; namely, conditional, preventable and non-preventable occurrences. Other types of occurrences, not discussed in this article, can also be accommodated.

Subclasses of Binary NP

Abstract: Binary NP consists of all sets of nite structures which are expressible in existential second order logic with second order quanti cation restricted to relations of arity 2. We look at semantical restrictions of binary NP, where the second order quanti ers range only over certain classes of relations. We consider mainly three types of classes of relations: unary functions, order relations and graphs with degree bounds. We show that many of these restrictions have the same expressive power and establish a 4-level strict hierarchy, represented by sets, permutations, unary functions and arbitrary binary relations, respectively.

A New Method for Automated Finite Model Building Exploiting Failures and Symmetries

Abstract: A method for building nite models is proposed. It combines enumeration of the set of interpretations on a nite domain with strategies in order to prune signiicantly the search space. The main new ideas underlying our method are to beneet from symmetries and from the information extracted from the structure of the problem and from failures of model veriication tests. The algorithms formalizing the approach are given and the standard properties (termination, completeness, and soundness) are proven. The method can deal with rst-order logic with equality. In contrast to existing ones, it does not require to transform the initial problem into a normal form and can be easily extended to other logics. Experimental results and comparisons with related works are reported.

A Relevant Analysis of Natural Deduction

Abstract: Linear and other relevant logics have been studied widely in mathematical, philosophical and computational logic. We describe a logical framework, RLF, for defining natural deduction presentations of such logics. RLF consists in a language togeth er, in a manner similar to that of Harper, Honsell and Plotkin’s LF, with a representation mec hanism: the language of RLF is the λΛ-calculus; the representation mechanism is judgements-as -type , developed for relevant logics. The λΛ-calculus type theory is a first-order dependent type theory with two kinds of dependent function spaces: a linear one and an intuitionistic one. We study a natural deduction presentation of the type theory and establish the required p oof-theoretic meta-theory. The RLF framework is a conservative extension of LF. We show that RLF uniformly encodes (fragments of) intuitionistic linear logic, Curry’sλI -calculus and ML with references. We describe the Curry-Howard-de Bruijn correspondence of t heλΛ-calculus with a structural fragment of O’Hearn and Pym’s logic BI of bunched implicatio ns. We show that a categorical semantics of the λΛ-calculus is given by Kripke resource models, which are a monoid-indexed set of Kripke functors. The index ing monoid is seen as providing an account of resource consumption. The models can be seen as a indexed formulation of categorical models of Read’s bunches. We also study a Gentzenized version of the λΛ-calculus, and prove a cut-elimination theorem for it. Submitted for the degree of Doctor of Philosophy Queen Mary and Westfield College University of London April, 1999

Computation of Prime Implicants using Matrix and Paths

Abstract: In this paper, an efficient algorithm to compute the set of prime implicants of a prepositional formula in Conjunctive Normal Form (CNF) is presented. The proposed algorithm uses a concept of representing the formula as a binary matrix and computing paths through the matrix as implicants. The algorithm finds the prime implicants as the prime paths using the divide-and-conquer technique. The proposed algorithm can be used for knowledge compilation, Clause Maintenance Systems where the knowledge base is prepositional formulae. Moreover, the algorithm is easily adaptable to the incremental mode of computation where an earlier formula is updated by a set of clauses.

Uniform Provability in Classical Logic

Abstract: Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We investigate the relevance of this uniform proof notion to structuring proof search in classical logic. A logical language in whose context provability is equivalent to uniform provability admits of a goal-directed proof procedure that interprets logical symbols as search directives whose meanings are given by the corresponding inference rules. While this uniform provability property does not hold directly of classical logic, we show that it holds of a fragment of it that only excludes essentially positive occurrences of universal quantifiers under a modest, sound, modification to the set of assumptions: the addition to them of the negation of the formula being proved. We further note that all uses of the added formula can be factored into certain derived rules. The resulting proof system and the uniform provability property that holds of it are used to outline a proof procedure for classical logic. An interesting aspect of this proof procedure is that it incorporates within it previously proposed mechanisms for dealing with disjunctive information in assumptions and for handling hypotheticals. Our analysis sheds light on the relationship between these mechanisms and the notion of uniform proofs.

Extensions for Open Default Theories via the Domain Closure Assumption

Abstract: In this paper we analyze the semantical definition of extensions for open default theories. We argue that this definition reflects the domain closure assumption and show how the domain closure assumption for countable and finite domains can be expressed in first-order default logic extended with the Carnap rule of inference. Also we give examples of the domain dependence of extensions for open default theories. In particular, we show that such extensions do not possess the minimality property.

Reasoning About Set Constraints Applied to Tractable Inference in Instutionstic Logic

Abstract: Automated reasoning about sets has received a considerable amount of interest in the literature. Techniques for such reasoning have been used in, for instance, analyses of programming languages, terminological logics and spatial reasoning. In this paper, we identify a new class of set constraints where checking satissability is tractable (i.e. polynomial-time). We show how to use this tractability result for constructing a new tractable fragment of intuitionistic logic. Furthermore, we prove NP-completeness of several other cases of reasoning about sets.

Applying the Mu-Calculus in Planning and Reasoning about Action

Abstract: Planning algorithms have traditionally been geared toward achievement goals in single-agent environments. Such algorithms essentially produce plans to reach one of a specified set of states. More general approaches for planning based on temporal logic (TL) are emerging. Current approaches tend to use linear TL, and can handle sets of sequences of states. However, they assume deterministic actions with all changes effected solely by one agent. By contrast, we use a branching model of time that can express concurrent actions by multiple agents and the environment, leading to nondeterministic effects of an agent’s actions. For this reason, we view plans not as sequences of actions, but as decision graphs describing the agent’s actions in different situations. Thus, although we consider single-agent decision graphs, our approach is better suited to multiagent systems. We also consider an expressive formalism, which allows a wider variety of goals, including achievement and maintenance goals. Achievement corresponds to traditional planning, but maintenance is more powerful than traditional maintenance goals, and may require nonterminating plans. To formalize decision graphs requires a means to “alternate” the agent’s and the environment’s choices. From logics of program, we introduce the propositional mu-calculus, which has operators for least and greatest fixpoints. We give a semantics, a fixpoint characterization, and an algorithm to compute decision graphs.

Optimized Encodings of Fragments of Type Theory in First-order Logic

Abstract: The paper presents sound and complete translations of several fragments of Martin-Lof's monomorphic type theory to first order predicate calculus. The translations are optimised for the purpose of automated theorem proving in the mentioned fragments. The implementation of the theorem prover Gandalf and several experimental results are described.

Adding the Everywhere Operator to Propositional Logic

Abstract: Sound and complete modal propositional logic C is presented, in which "P" has the interpretation "P is true in all states" The interpretation is already known as the Carnapian extension of S5 A new axiomatization for C provides two insights First, introducing an inference rule "textual substitution" allows seamless integration of the propositional and modal parts of the logic, giving a more practical system for writing formal proofs Second, the two following approaches to axiomatizing a logic are shown to be not equivalent: (i) give axiom schemes that denote an infinite number of axioms and (ii) write a finite number of axioms in terms of propositional variables and introduce a substitution inference rule

Tableau Methods for Formal Verification of Multi-Agent Distributed Systems

Abstract: Formal verification is a key step in the development of trusted and reliable multi-agent distributed systems. This is particularly relevant when security concerns such as privacy, integrity and availability impose limitations on the operations that can be performed on sensitive data. The aim of access control is to limit what agents (humans, programs, softbots, etc.) of distributed systems can do directly or indirectly by delegating their powers and tasks. As the size of the systems and the sensitivity of data increase, the availability of automated reasoning methods becomes essential for logical analysis of access control. This paper presents a prefixed tableau method for the calculus of access control developed at the Digital System Research Center by Abadi, Lampson et. al. This calculus is particularly interesting for a number of reasons. At first it was the basis for the development and the verification of an implemented system. Second, it poses many technical challenges for classical modal tableaux: it lacks the tree-model property, has some features of the universal modality, and can introduce delegation certificates between agents “on-the-fly” not compilable into axiom schemata.

Simplification of Many-Valued Logic Formulas Using Anti-Links

Abstract: We present the theoretical foundations of the many-valued generalization of a technique for simplifying large non-clausal formulas in propositional logic, that is called removal of anti-links. Possible applications of anti-links include computation of prime implicates of large non-clausal formulas as required, for example, in diagnosis. Anti-links do not compute any normal form of a given formula themselves, rather, they remove certain forms of redundancy from formulas in negation normal form (NNF). Their main advantage is that no clausal normal form has to be computed in order to remove redundant parts of a formula. In this paper, we de ne an anti-link operation on a generic language for expressing many-valued logic formulas called signed NNF and we show that all interesting properties of two-valued anti-links generalize to the many-valued setting, although in a non-trivial way.

Intuitionistic Propositional Logic with only Equivalence has no Interpolation

Abstract: We will show in this paper that there is no interpolation theorem for the fragment of pure equivalence in intuitionistic propositional logic. The computer program that was used to calculate the counterexample by computations on a nite Kripke model is brieey sketched.

Saturated Formulas in Full Linear Logic

Abstract: In this note, we show by a proof-theoretical argument that in full linear logic the set of formulas for which contraction and weakening are admissible (the set of saturated formulas) does not coincide (up to equivalences) with the set of exponentiated formulas. This solves an open problem of Schellinx.