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Categorical and Kripke Semantics for Constructive S4 Modal Logic
 In International Workshop on Computer Science Logic, CSL’01, L. Fribourg, Ed. Lecture Notes in Computer Science
, 2001
"... We consider two systems of constructive modal logic which are computationally motivated. Their modalities admit several computational interpretations and are used to capture intensional features such as notions of computation, constraints, concurrency, etc. Both systems have so far been studied m ..."
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Cited by 36 (1 self)
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We consider two systems of constructive modal logic which are computationally motivated. Their modalities admit several computational interpretations and are used to capture intensional features such as notions of computation, constraints, concurrency, etc. Both systems have so far been studied mainly from typetheoretic and categorytheoretic perspectives, but Kripke models for similar systems were studied independently. Here we bring these threads together and prove duality results which show how to relate Kripke models to algebraic models and these in turn to the appropriate categorical models for these logics.
Categorical and Kripke Semantics for Constructive Modal Logics
, 2001
"... We consider two systems of constructive modal logic which are computationally motivated. Their modalities admit several computational interpretations and are used to capture intensional features such as notions of computation, constraints, concurrency design, etc. Both systems have so far been studi ..."
Abstract

Cited by 7 (3 self)
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We consider two systems of constructive modal logic which are computationally motivated. Their modalities admit several computational interpretations and are used to capture intensional features such as notions of computation, constraints, concurrency design, etc. Both systems have so far been studied mainly from a typetheoretic and categorytheoretic perspectives, but Kripke models for similar systems were studied independently. Here we bring these threads together and prove duality results which show how to relate Kripke models to algebraic models and these in turn to the appropriate categorical models for these logics.
Journal of Applied Logic •• • (••••) •••–•••
"... JAL:m1a v 1.40 Prn:15/07/2005; 8:08 jal71 by:SL p. 1 ..."
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Modal Logics with Existential Modality, Finiteiteration Modality, and Intuitionistic Base: Decidability and Completeness
, 2005
"... This thesis investigates some modal logics that have been found to be useful in modelling computational phenomena and, therefore, of interest to theoretical computer sciencenamely, modal intuitionistic logics, logics with finiteiteration modality, and logics with existential modality. We prove a ..."
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This thesis investigates some modal logics that have been found to be useful in modelling computational phenomena and, therefore, of interest to theoretical computer sciencenamely, modal intuitionistic logics, logics with finiteiteration modality, and logics with existential modality. We prove a number of new general results concerning these logics. In particular, in chapter 3, we prove a general decidability result for intuitionistic modal logics through embedding them into the twovariable monadic secondorder guarded fragment GF mon with certain conditions imposed on relations occurring in GF mon formulas. In chapter 4, we prove the analogue of Makinson theorem for logics with finiteiteration modality, that is that every consistent logic in this language is either a sublogic of the logic of a Kripke frame containing a single reflexive point or a sublogic of the logic of a Kripke frame containing a single irreflexive point; the byproduct of the theorem is the decidability of the problem of consistency for effectively finitely axiomatizable logics with finiteiteration modality. In chapter 5, we prove completeness of Hilbertstyle axiomatizations of three logics whose language contains an existential modality ###: the minimal normal logic with ###, K# ; its deterministic extension DK# ; and the logic that is CPDL (converse PDL) with a single nominal and ### (this logic is known from the literature as PDL ). Apart from the presentation of the abovementioned results, the thesis contains, in chapter 2, an overview of background material on modal logics and guarded fragments; this overview can also be read as a concise survey of the field of guarded fragments.