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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....
Category Structures
 COMPUTATIONAL LINGUISTICS
, 1988
"... This paper outlines a simple and general notion of syntactic category on a metatheoretical level, independent of the notations and substantive claims of any particular grammatical framework. We define a class of formal objects called "category structures" where each such object provides a constructi ..."
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Cited by 30 (2 self)
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This paper outlines a simple and general notion of syntactic category on a metatheoretical level, independent of the notations and substantive claims of any particular grammatical framework. We define a class of formal objects called "category structures" where each such object provides a constructive definition for a space of syntactic categories. A unification operation and subsumption and identity relations are defined for arbitrary syntactic categories. In addition, a formal language for the statement of constraints on categories is provided. By combining a category structure with a set of constraints, we show that one can define the category systems of several wellknown grammatical frameworks: phrase structure grammar, tagmemics, augmented phrase structure grammar, relational grammar, transformational grammar, generalized phrase structure grammar, systemic grammar, categorial grammar, and indexed grammar. The problem' of checking a category for conformity to constraints is shown to be soivable in linear time. This work provides in effect a unitary class of data structures for the representation of syntactic categories in a range of diverse grammatical frameworks. Using such data structures should make it possible for various pseudoissues in natural language processing research to be avoided. We conclude by examining the questions posed by setvalued features and sharing of values between distinct feature specifications, both of which fall outside the scope of the formal system developed in this paper
Epistemic logics and their game theoretic applications: Introduction. Economic Theory
, 2002
"... ..."
Labelled Tableaux for NonNormal Modal Logics
 In Sixth Conference of the Italian Association for Arti Intelligence, AI*IA '99
, 2000
"... In this paper we show how to extend \KEM, a tableaulike proof system for normal modal logic, in order to deal with classes of nonnormal modal logics, such as monotonic and regular, in a uniform and modular way. ..."
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Cited by 11 (6 self)
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In this paper we show how to extend \KEM, a tableaulike proof system for normal modal logic, in order to deal with classes of nonnormal modal logics, such as monotonic and regular, in a uniform and modular way.
A quantified logic of evidence
 Annals of Pure and Applied Logic
, 2008
"... A propositional logic of explicit proofs, LP, was introduced in [2], completing a project begun long ago by Gödel, [13]. In fact, LP can be looked at in a more general way, as a logic of explicit evidence, and there have been several papers along these lines. A major result about LP is the Realizati ..."
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Cited by 7 (0 self)
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A propositional logic of explicit proofs, LP, was introduced in [2], completing a project begun long ago by Gödel, [13]. In fact, LP can be looked at in a more general way, as a logic of explicit evidence, and there have been several papers along these lines. A major result about LP is the Realization Theorem, that says any theorem of S4 can be converted into a theorem of LP by some replacement of necessitation symbols with explicit proof terms. Thus the necessitation operator of S4 can be seen as a kind of implicit existential quantifier: there exists a proof term (explicit evidence) such that.... In this paper, quantification over evidence is introduced into LP, and it is shown that the connection between S4 necessitation and the existential quantifier becomes an explicit one. The extension of LP with quantifiers is called QLP. A semantics and an axiom system for QLP are given, soundness and completeness are established, and several results are proved relating QLP to LP and to S4. 1
Definability and Commonsense Reasoning
 ARTIF. INTELL
, 1997
"... The definition of concepts is a central problem in commonsense reasoning. Many themes in nonmonotonic reasoning concern implicit and explicit definability. Implicit definability in nonmonotonic logic is always relative to the context  the current theory of the world. We show that fixed point equati ..."
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Cited by 6 (3 self)
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The definition of concepts is a central problem in commonsense reasoning. Many themes in nonmonotonic reasoning concern implicit and explicit definability. Implicit definability in nonmonotonic logic is always relative to the context  the current theory of the world. We show that fixed point equations provide a generalization of explicit definability, which correctly captures the relativized context. Theories expressed within this logical framework provide implicit definitions of concepts. Moreover, it is possible to derive these fixed points entirely within the logic.
Modal Provability Foundations for Negation as Failure I, 4 th draft
 Extensions of Logic Programming: International Workshop, Tübingen FRG
, 1989
"... This paper is a contribution to the foundation of negation by failure. It presents a view of negation by failure as a modal provability notion. Negation by failure is a central notion in Logic Programming and is used extensively in practice. There are various attempts at its foundations each with it ..."
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Cited by 5 (1 self)
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This paper is a contribution to the foundation of negation by failure. It presents a view of negation by failure as a modal provability notion. Negation by failure is a central notion in Logic Programming and is used extensively in practice. There are various attempts at its foundations each with its own difficulties
Modal Non Monotonic Reasoning Via Boxed Fixed Points
 6TH INTERNATIONAL WORKSHOP ON NONMONOTONIC REASONING
, 1996
"... In [ACGP96] boxed expansions were introduced and new modal non monotonic logics, not contained in the families of logics identified by Marek, Schwarz and Truszczynski, was found to embed Reiter's default logic. Besides S4f , indeed also KD4Z was shown to be adequate to represent default logic ..."
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Cited by 2 (2 self)
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In [ACGP96] boxed expansions were introduced and new modal non monotonic logics, not contained in the families of logics identified by Marek, Schwarz and Truszczynski, was found to embed Reiter's default logic. Besides S4f , indeed also KD4Z was shown to be adequate to represent default logic. Besides
The Interpolation Theorem for IL and ILP
 Uppsala University
, 1998
"... In this article we establish interpolation for the minimal system of interpretability logic IL. We prove that arrow interpolation holds for IL and that turnstile interpolation and interpolation for the modality easily follow from this. Furthermore, these properties are extended to the system ILP. ..."
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Cited by 2 (0 self)
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In this article we establish interpolation for the minimal system of interpretability logic IL. We prove that arrow interpolation holds for IL and that turnstile interpolation and interpolation for the modality easily follow from this. Furthermore, these properties are extended to the system ILP. The related issue of Beth Definability is also addressed. As usual, the arrow interpolation property implies the Beth property. From the latter it follows via an argumentation which is standard in provability logic, that IL has the fixed point property. Finally we observe that a general result of Maksimova [11] for provability logics can be extended to interpretability logics, implying that all extensions of IL have the Beth property. Keywords Interpretability Logic, Interpolation Properties, Beth Property, Fixed Point Property. 1 Introduction 1.1 Some History Interpretability logics are extensions of provability logics introduced by Visser in [15]. There the modal logics IL, ILM and ILP a...