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Hybrid Logics
"... This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur ..."
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Cited by 34 (10 self)
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This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur
Qualitative SpatioTemporal Representation and Reasoning: A Computational Perspective
 Exploring Artifitial Intelligence in the New Millenium
, 2001
"... this paper argues for the rich world of representation that lies between these two extremes." Levesque and Brachman (1985) 1 Introduction Time and space belong to those few fundamental concepts that always puzzled scholars from almost all scientific disciplines, gave endless themes to science fict ..."
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Cited by 30 (11 self)
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this paper argues for the rich world of representation that lies between these two extremes." Levesque and Brachman (1985) 1 Introduction Time and space belong to those few fundamental concepts that always puzzled scholars from almost all scientific disciplines, gave endless themes to science fiction writers, and were of vital concern to our everyday life and commonsense reasoning. So whatever approach to AI one takes [ Russell and Norvig, 1995 ] , temporal and spatial representation and reasoning will always be among its most important ingredients (cf. [ Hayes, 1985 ] ). Knowledge representation (KR) has been quite successful in dealing separately with both time and space. The spectrum of formalisms in use ranges from relatively simple temporal and spatial databases, in which data are indexed by temporal and/or spatial parameters (see e.g. [ Srefik, 1995; Worboys, 1995 ] ), to much more sophisticated numerical methods developed in computational geom
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.
Modal Logic: A Semantic Perspective
 ETHICS
, 1988
"... This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames. We want the reader to gain an intuitive appreciation of this perspective, and a firm grasp of the key technical ideas (such as bisimul ..."
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Cited by 13 (1 self)
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This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames. We want the reader to gain an intuitive appreciation of this perspective, and a firm grasp of the key technical ideas (such as bisimulations) which underly it. We introduce the syntax and semantics of basic modal logic, discuss its expressivity at the level of models, examine its computational properties, and then consider what it can say at the level of frames. We then move beyond the basic modal language, examine the kinds of expressivity offered by a number of richer modal logics, and try to pin down what it is that makes them all ‘modal’. We conclude by discussing an example which brings many of the ideas we discuss into play: games.
Modal languages for topology: Expressivity and definability, in "Annals of Pure and
 n o 12, 2009, p. 146170, http://hal.inria.fr/inria00424693/en/ GENL. International PeerReviewed Conference/Proceedings
"... In this paper we study the expressive power and definability for (extended) modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the GoldblattThomason definability theorem in terms of the well established firstorder top ..."
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Cited by 12 (3 self)
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In this paper we study the expressive power and definability for (extended) modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the GoldblattThomason definability theorem in terms of the well established firstorder topological language Lt.
Monotonic Modal Logics
, 2003
"... Monotonic modal logics form a generalization of normal modal logics... ..."
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Cited by 11 (0 self)
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Monotonic modal logics form a generalization of normal modal logics...
A New Proof of Completeness of S4 with Respect to the Real Line
, 2002
"... It was proved in McKinsey and Tarski [7] that every finite wellconnected closure algebra is embedded into the closure algebra of the power set of the real line R. Pucket [10] extended this result to all finite connected closure algebras by showing that there exists an open map from R to any fini ..."
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Cited by 8 (1 self)
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It was proved in McKinsey and Tarski [7] that every finite wellconnected closure algebra is embedded into the closure algebra of the power set of the real line R. Pucket [10] extended this result to all finite connected closure algebras by showing that there exists an open map from R to any finite connected topological space. We simplify his proof considerably by using the correspondence between finite topological spaces and finite quasiordered sets. As a consequence, we obtain that the propositional modal system S4 of Lewis is complete with respect to Boolean combinations of countable unions of convex subsets of R, which is strengthening of McKinsey and Tarski's original result. We also obtain that the propositional modal system Grz of Grzegorczyk is complete with respect to Boolean combinations of open subsets of R. Finally, we show that McKinsey and Tarski's result can not be extended to countable connected closure algebras by proving that no countable Alexandro# space containing an infinite ascending chain is an open image of R.
Topodistance: Measuring the Difference between Spatial Patterns
"... A framework to deal with spatial patterns at the qualitative level of mereotopology is proposed. The main... ..."
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Cited by 2 (1 self)
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A framework to deal with spatial patterns at the qualitative level of mereotopology is proposed. The main...
Euclidean Hierarchy in Modal Logic
 Studia Logica
, 2002
"... For an Euclidean space R , let L n denote the modal logic of chequered . For every n 1, we characterize L n using the more familiar Kripke semantics, thus implying that each L n is a tabular logic over the wellknown modal system Grz of Grzegorczyk. ..."
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Cited by 2 (1 self)
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For an Euclidean space R , let L n denote the modal logic of chequered . For every n 1, we characterize L n using the more familiar Kripke semantics, thus implying that each L n is a tabular logic over the wellknown modal system Grz of Grzegorczyk.
Computing Spatial Similarity by Games
 Conference of the Italian Association for Artificial Intelligence (AI*IA01), number 2175 in Lecture Notes in Artificial Intelligence
, 2001
"... In: F. Esposito (Eds.), Congress of the Italian Association for Artificial Intelligence (AI*IA 2001), LNAI 2175, pp. 99110, Springer, 2001. ..."
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In: F. Esposito (Eds.), Congress of the Italian Association for Artificial Intelligence (AI*IA 2001), LNAI 2175, pp. 99110, Springer, 2001.