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Tableau Methods for Modal and Temporal Logics
, 1995
"... This document is a complete draft of a chapter by Rajeev Gor'e on "Tableau Methods for Modal and Temporal Logics" which is part of the "Handbook of Tableau Methods", edited by M. D'Agostino, D. Gabbay, R. Hahnle and J. Posegga, to be published in 1998 by Kluwer, Dordrecht. Any comments and correctio ..."
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Cited by 125 (20 self)
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This document is a complete draft of a chapter by Rajeev Gor'e on "Tableau Methods for Modal and Temporal Logics" which is part of the "Handbook of Tableau Methods", edited by M. D'Agostino, D. Gabbay, R. Hahnle and J. Posegga, to be published in 1998 by Kluwer, Dordrecht. Any comments and corrections are highly welcome. Please email me at rpg@arp.anu.edu.au The latest version of this document can be obtained via my WWW home page: http://arp.anu.edu.au/ Tableau Methods for Modal and Temporal Logics Rajeev Gor'e Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 Syntax and Notational Conventions . . . . . . . . . . . . 3 2.2 Axiomatics of Modal Logics . . . . . . . . . . . . . . . . 4 2.3 Kripke Semantics For Modal Logics . . . . . . . . . . . . 5 2.4 Known Correspondence and Completeness Results . . . . 6 2.5 Logical Consequence . . . . . . . . . . . . . . . . . . . . 8 2....
An Overview of Temporal and Modal Logic Programming
 Proc. First Int. Conf. on Temporal Logic  LNAI 827
, 1994
"... . This paper presents an overview of the development of the field of temporal and modal logic programming. We review temporal and modal logic programming languages under three headings: (1) languages based on interval logic, (2) languages based on temporal logic, and (3) languages based on (multi)mo ..."
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Cited by 60 (6 self)
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. This paper presents an overview of the development of the field of temporal and modal logic programming. We review temporal and modal logic programming languages under three headings: (1) languages based on interval logic, (2) languages based on temporal logic, and (3) languages based on (multi)modal logics. The overview includes most of the major results developed, and points out some of the similarities, and the differences, between languages and systems based on diverse temporal and modal logics. The paper concludes with a brief summary and discussion. Categories: Temporal and Modal Logic Programming. 1 Introduction In logic programming, a program is a set of Horn clauses representing our knowledge and assumptions about some problem. The semantics of logic programs as developed by van Emden and Kowalski [96] is based on the notion of the least (minimum) Herbrand model and its fixedpoint characterization. As logic programming has been applied to a growing number of problem domai...
The Substitutional Framework for Sorted Deduction: Fundamental Results on Hybrid Reasoning
 Artificial Intelligence
, 1990
"... Researchers in artificial intelligence have recently been taking great interest in hybrid representations, among them sorted logicslogics that link a traditional logical representation to a taxonomic (or sort) representation such as those prevalent in semantic networks. This paper introduces a ge ..."
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Cited by 50 (9 self)
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Researchers in artificial intelligence have recently been taking great interest in hybrid representations, among them sorted logicslogics that link a traditional logical representation to a taxonomic (or sort) representation such as those prevalent in semantic networks. This paper introduces a general frameworkthe substitutional frameworkfor integrating logical deduction and sortal deduction to form a deductive system for sorted logic. This paper also presents results that provide the theoretical underpinnings of the framework. A distinguishing characteristic of a deductive system that is structured according to the substitutional framework is that the sort subsystem is invoked only when the logic subsystem performs unification, and thus sort information is used only in determining what substitutions to make for variables. Unlike every other known approach to sorted deduction, the substitutional framework provides for a systematic transformation of unsorted deductive systems ...
MSPASS: Modal Reasoning by Translation and FirstOrder Resolution
, 2000
"... mspass is an extension of the firstorder theorem prover spass, which can be used as a modal logic theorem prover, a theorem prover for description logics and a theorem prover for the relational calculus. ..."
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Cited by 36 (4 self)
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mspass is an extension of the firstorder theorem prover spass, which can be used as a modal logic theorem prover, a theorem prover for description logics and a theorem prover for the relational calculus.
Modality in Dialogue: Planning, Pragmatics and Computation
, 1998
"... Natural language generation (NLG) is first and foremost a reasoning task. In this reasoning, a system plans a communicative act that will signal key facts about the domain to the hearer. In generating action descriptions, this reasoning draws on characterizations both of the causal properties of the ..."
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Cited by 36 (9 self)
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Natural language generation (NLG) is first and foremost a reasoning task. In this reasoning, a system plans a communicative act that will signal key facts about the domain to the hearer. In generating action descriptions, this reasoning draws on characterizations both of the causal properties of the domain and the states of knowledge of the participants in the conversation. This dissertation shows how such characterizations can be specified declaratively and accessed efficiently in NLG. The heart of this dissertation is a study of logical statements about knowledge and action in modal logic. By investigating the prooftheory of modal logic from a logic programming point of view, I show how many kinds of modal statements can be seen as straightforward instructions for computationally manageable search, just as Prolog clauses can. These modal statements provide sufficient expressive resources for an NLG system to represent the effects of actions in the world or to model an addressee whose knowledge in some respects exceeds and in other respects falls short of its own. To illustrate the use of such statements, I describe how the SPUD sentence planner exploits a modal knowledge base to
Resolution for Temporal Logics of Knowledge
 Journal of Logic and Computation
, 1998
"... A resolution based proof system for a temporal logic of knowledge is presented and shown to be correct. Such logics are useful for proving properties of distributed and multiagent systems. Examples are given to illustrate the proof system. An extension of the basic system to the multimodal case is ..."
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Cited by 35 (18 self)
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A resolution based proof system for a temporal logic of knowledge is presented and shown to be correct. Such logics are useful for proving properties of distributed and multiagent systems. Examples are given to illustrate the proof system. An extension of the basic system to the multimodal case is given and illustrated using the `muddy children problem'. 1 Introduction Temporal logics have been shown to have many applications in computer science and artificial intelligence. For example, they are used in the specification and verification of reactive systems [28], in temporal query languages [8], executable logics [18] and for reasoning about action [36]. For some applications, however, logics containing connectives that operate over just the one modal dimension of time do not provide sufficient expressive power. For such applications, it is necessary to provide connectives that allow us to represent the properties of different modal dimensions in the same logic. In this paper, we co...
A General Framework for Modal Deduction
 AGENTS AND THE SEMANTIC WEB. IEEE INTELLIGENT SYSTEMS
, 1991
"... A general method of automated modal logic theorem proving is discussed and illustrated. This method is based on the substitutional framework for the development of systems for hybrid reasoning. Sentences in modal logic are translated into a constraint logic in which the constraints represent the con ..."
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Cited by 24 (7 self)
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A general method of automated modal logic theorem proving is discussed and illustrated. This method is based on the substitutional framework for the development of systems for hybrid reasoning. Sentences in modal logic are translated into a constraint logic in which the constraints represent the connections between worlds in the possible world semantics for modal logic. Deduction in the constraint logic is performed by a nonmodal deductive system which has been systematically enhanced with specialpurpose constraint processing mechanisms. The result is a modal logic theorem prover, whose soundness and completeness is an immediate consequence of the correctness of the nonmodal deductive system and some general results on constraint deduction. The framework achieves significant generality in that it provides for the extension of a wide range of nonmodal systems to corresponding modal systems and that this can be done for a wide range of modal logics.
A Tableau Calculus for Multimodal Logics and Some (Un)Decidability Results
 IN PROC. OF TABLEAUX98
, 1998
"... In this paper we present a prefixed analytic tableau calculus for a class of normal multimodal logics and we present some results about decidability and undecidability of this class. The class is characterized by axioms of the form [t 1 ] : : : [t n ]' oe [s1 ] : : : [sm ]', called inclusion axio ..."
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Cited by 24 (8 self)
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In this paper we present a prefixed analytic tableau calculus for a class of normal multimodal logics and we present some results about decidability and undecidability of this class. The class is characterized by axioms of the form [t 1 ] : : : [t n ]' oe [s1 ] : : : [sm ]', called inclusion axioms, where the t i 's and s j 's are constants. This class of logics, called grammar logics, was introduced for the first time by Farinas del Cerro and Penttonen to simulate the behaviour of grammars in modal logics, and includes some wellknown modal systems. The prefixed tableau method is used to prove the undecidability of modal systems based on unrestricted, context sensitive, and context free grammars. Moreover, we show that the class of modal logics, based on rightregular grammars, are decidable by means of the filtration methods, by defining an extension of the FischerLadner closure.
Using Resolution for Testing Modal Satisfiability and Building Models
, 2000
"... . This paper presents a translationbased resolution decision procedure for the multimodal logic K (m) (\; [; ^) dened over families of relations closed under intersection, union and converse. The relations may satisfy certain additional frame properties. Dierent from previous resolution decision p ..."
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Cited by 23 (11 self)
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. This paper presents a translationbased resolution decision procedure for the multimodal logic K (m) (\; [; ^) dened over families of relations closed under intersection, union and converse. The relations may satisfy certain additional frame properties. Dierent from previous resolution decision procedures which are based on ordering renements our procedure is based on a selection renement, the derivations of which correspond to derivations of tableaux or sequent proof systems. This procedure has the advantage that it can be used both as a satisability checker and a model builder. We show that tableaux and sequentstyle proof systems can be polynomially simulated with our procedure. Furthermore, the nite model property follows for a number of extended modal logics. Keywords: modal logic, automated theorem proving, resolution decision procedures, tableaux proof systems, satisability testing, model generation, simulation, relative proof complexity, relative search space complex...