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53
Modal Logics for Qualitative Spatial Reasoning
, 1996
"... Spatial reasoning is essential for many AI applications. In most existing systems the representation is primarily numerical, so the information that can be handled is limited to precise quantitative data. However, for many purposes the ability to manipulate highlevel qualitative spatial information ..."
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Cited by 82 (12 self)
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Spatial reasoning is essential for many AI applications. In most existing systems the representation is primarily numerical, so the information that can be handled is limited to precise quantitative data. However, for many purposes the ability to manipulate highlevel qualitative spatial information in a flexible way would be extremely useful. Such capabilities can be proveded by logical calculi; and indeed 1storder theories of certain spatial relations have been given [20]. But computing inferences in 1storder logic is generally intractable unless special (domain dependent) methods are known. 0order modal logics provide an alternative representation which is more expressive than classical 0order logic and yet often more amenable to automated deduction than 1storder formalisms. These calculi are usually interpreted as propositional logics: nonlogical constants are taken as denoting propositions. However, they can also be given a nominal interpretation in which the constants stand...
Spatiotemporal representation and reasoning based on RCC8
 In Proceedings of the seventh Conference on Principles of Knowledge Representation and Reasoning, KR2000
, 2000
"... this paper is to introduce a hierarchy of languages intended for qualitative spatiotemporal representation and reasoning, provide these languages with topological temporal semantics, construct effective reasoning algorithms, and estimate their computational complexity. ..."
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Cited by 57 (10 self)
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this paper is to introduce a hierarchy of languages intended for qualitative spatiotemporal representation and reasoning, provide these languages with topological temporal semantics, construct effective reasoning algorithms, and estimate their computational complexity.
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 24 (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.
Combining Spatial and Temporal Logics: Expressiveness Vs. Complexity
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2004
"... In this paper, we construct and investigate a hierarchy of spatiotemporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic the spatial logics RCC8, BRCC8, S4 u and their fragments. The obtained results give ..."
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Cited by 20 (9 self)
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In this paper, we construct and investigate a hierarchy of spatiotemporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic the spatial logics RCC8, BRCC8, S4 u and their fragments. The obtained results give a clear picture of the tradeoff between expressiveness and `computational realisability' within the hierarchy. We demonstrate how di#erent combining principles as well as spatial and temporal primitives can produce NP, PSPACE, EXPSPACE, 2EXPSPACEcomplete, and even undecidable spatiotemporal logics out of components that are at most NP or PSPACEcomplete.
Intuitionistic modal logics as fragments of classical bimodal logics
, 1998
"... Gödel's translation of intuitionistic formulas into modal ones provides the wellknown embedding of intermediate logics into extensions of Lewis' system S4, which reflects and sometimes preserves such properties as decidability, Kripke completeness, the finite model property. In this paper ..."
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Cited by 19 (5 self)
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Gödel's translation of intuitionistic formulas into modal ones provides the wellknown embedding of intermediate logics into extensions of Lewis' system S4, which reflects and sometimes preserves such properties as decidability, Kripke completeness, the finite model property. In this paper we establish a similar relationship between intuitionistic modal logics and classical bimodal logics. We also obtain some general results on the finite model property of intuitionistic modal logics first by proving them for bimodal logics and then using the preservation theorem.
On the relation between intuitionistic and classical modal logics. Algebra and Logic
, 1996
"... Intuitionistic propositional logic Int and its extensions, known as intermediate or superintuitionistic logics, in many respects can be regarded just as fragments of classical modal logics containing S4. Atthe syntactical level, the Godel translation t embeds every intermediate logic L = Int+ into m ..."
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Cited by 16 (4 self)
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Intuitionistic propositional logic Int and its extensions, known as intermediate or superintuitionistic logics, in many respects can be regarded just as fragments of classical modal logics containing S4. Atthe syntactical level, the Godel translation t embeds every intermediate logic L = Int+ into modal log1 ics in the interval L = [ L = S4 t (); L=Grz t ()]. Semantically this is re ected by the fact that Heyting algebras are precisely the algebras of open elements of topological Boolean algebras. From the latticetheoretic standpoint the map is a homomorphism of the lattice of logics containing S4 onto the lattice of intermediate logics, while, according to the Blok{Esakia theorem, is an isomorphism of the latter onto the lattice of extensions of the Grzegorczyk system Grz. Atthe philosophical level the Godel translation provides a classical interpretation of the intuitionistic connectives. And from the technical point of view this embedding is a powerful tool for transferring various kinds of results from intermediate logics to modal ones and back via preservation theorems.
HennessyMilner classes and process algebra
 Modal Logic and Process Algebra
, 1995
"... This paper studies HennessyMilner classes, classes of Kripke models where modallogical equivalence coincides with bisimulation. Concepts associated with these classes in the literature (Goldblatt [6], Visser [8]) are studied and compared and the structure of the collection of maximal HennessyMiln ..."
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Cited by 15 (1 self)
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This paper studies HennessyMilner classes, classes of Kripke models where modallogical equivalence coincides with bisimulation. Concepts associated with these classes in the literature (Goldblatt [6], Visser [8]) are studied and compared and the structure of the collection of maximal HennessyMilner classes is investigated (how manyare there, what is their intersection?). The insights into these classes are applied to process algebra. This results in a HennessyMilner process algebra for a nontrivial process language, whose standard graphsemantics is not HennessyMilner. 1
Ultrafilter extensions for coalgebras
 In Algebra and Coalgebra in Computer Science, volume 3629 of LNCS
, 2005
"... Abstract. This paper studies finitary modal logics as specification languages for Setcoalgebras (coalgebras on the category of sets) using Stone duality. It is wellknown that Setcoalgebras are not semantically adequate for finitary modal logics in the sense that bisimilarity does not in general co ..."
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Cited by 13 (6 self)
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Abstract. This paper studies finitary modal logics as specification languages for Setcoalgebras (coalgebras on the category of sets) using Stone duality. It is wellknown that Setcoalgebras are not semantically adequate for finitary modal logics in the sense that bisimilarity does not in general coincide with logical equivalence.