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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 ..."
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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
Monodic temporal resolution
 ACM Transactions on Computational Logic
, 2003
"... Until recently, FirstOrder Temporal Logic (FOTL) has been only partially understood. While it is well known that the full logic has no finite axiomatisation, a more detailed analysis of fragments of the logic was not previously available. However, a breakthrough by Hodkinson et al., identifying a f ..."
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Cited by 27 (15 self)
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Until recently, FirstOrder Temporal Logic (FOTL) has been only partially understood. While it is well known that the full logic has no finite axiomatisation, a more detailed analysis of fragments of the logic was not previously available. However, a breakthrough by Hodkinson et al., identifying a finitely axiomatisable fragment, termed the monodic fragment, has led to improved understanding of FOTL. Yet, in order to utilise these theoretical advances, it is important to have appropriate proof techniques for this monodic fragment. In this paper, we modify and extend the clausal temporal resolution technique, originally developed for propositional temporal logics, to enable its use in such monodic fragments. We develop a specific normal form for monodic formulae in FOTL, and provide a complete resolution calculus for formulae in this form. Not only is this clausal resolution technique useful as a practical proof technique for certain monodic classes, but the use of this approach provides us with increased understanding of the monodic fragment. In particular, we here show how several features of monodic FOTL can be established as corollaries of the completeness result for the clausal temporal resolution method. These include definitions of new decidable monodic classes, simplification of existing monodic classes by reductions, and completeness of clausal temporal resolution in the case of
TeMP: A Temporal Monodic Prover
 In Proc. IJCAR04, LNAI
, 2004
"... We present TeMPthe first experimental system for testing validity of monodic temporal logic formulae. The prover implements finegrained temporal resolution. The core operations required by the procedure are performed by an efficient resolutionbased prover for classical firstorder logic. ..."
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Cited by 20 (11 self)
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We present TeMPthe first experimental system for testing validity of monodic temporal logic formulae. The prover implements finegrained temporal resolution. The core operations required by the procedure are performed by an efficient resolutionbased prover for classical firstorder logic.
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.
Monodic Packed Fragment With Equality is Decidable
 Studia Logica
, 2001
"... We prove decidability of satisfiability of sentences of the monodic packed fragment of firstorder temporal logic with equality and connectives Until and Since, in models with various flows of time and domains of arbitrary cardinality. We also prove decidability over models with finite domains, over ..."
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Cited by 20 (1 self)
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We prove decidability of satisfiability of sentences of the monodic packed fragment of firstorder temporal logic with equality and connectives Until and Since, in models with various flows of time and domains of arbitrary cardinality. We also prove decidability over models with finite domains, over flows of time including the real order.
Temporalising Tableaux
 STUDIA LOGICA
, 2004
"... As a remedy for the bad computational behaviour of firstorder temporal logic (FOTL), it has recently been proposed to restrict the application of temporal operators to formulas with at most one free variable thereby obtaining socalled monodic fragments of FOTL. In this paper, we are concerned with ..."
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Cited by 17 (5 self)
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As a remedy for the bad computational behaviour of firstorder temporal logic (FOTL), it has recently been proposed to restrict the application of temporal operators to formulas with at most one free variable thereby obtaining socalled monodic fragments of FOTL. In this paper, we are concerned with constructing tableau algorithms for monodic fragments based on decidable fragments of firstorder logic like the twovariable fragment or the guarded fragment. We present a general framework that shows how existing decision procedures for firstorder fragments can be used for constructing a tableau algorithm for the corresponding monodic fragment of FOTL.
Equality and Monodic FirstOrder Temporal Logic
 Studia Logica
, 2002
"... It has been shown recently that monodic firstorder temporal logic without functional symbols but with equality is incomplete, i.e. the set of the valid formulae of this logic is not recursively enumerable. In this paper we show that an even simpler fragment consisting of monodic monadic twovari ..."
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Cited by 14 (7 self)
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It has been shown recently that monodic firstorder temporal logic without functional symbols but with equality is incomplete, i.e. the set of the valid formulae of this logic is not recursively enumerable. In this paper we show that an even simpler fragment consisting of monodic monadic twovariable formulae is not recursively enumerable.
TRP ++ : A temporal resolution prover
 In Collegium Logicum
, 2002
"... this paper. 2 Basics of PLTL Let P be a set of propositional variables. The set of formulae of propositional linear time logic PLTL (over P) is inductively defined as follows: (i) ? is a formula of PLTL, (ii) every propositional variable of P is a formula of PLTL, (iii) if ' and / are formula ..."
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Cited by 12 (5 self)
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this paper. 2 Basics of PLTL Let P be a set of propositional variables. The set of formulae of propositional linear time logic PLTL (over P) is inductively defined as follows: (i) ? is a formula of PLTL, (ii) every propositional variable of P is a formula of PLTL, (iii) if ' and / are formulae of PLTL, then :' and (' /) are formulae of PLTL, and (iv) if ' and / are formulae of PLTL, then #' (in the next moment of time ' is true), 3' (sometimes in the future ' is true), 2' (always in the future ' is true), (' U /) (' is true until / is true), and (' W /) (' is true unless / is true) are formulae of PLTL. Other Boolean connectives including ?, , !, and $ are defined using ?, :, and