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96
Temporal Concurrent Constraint Programming: Denotation, Logic and Applications
, 2002
"... The tcc model is a formalism for reactive concurrent constraint programming. We present a model of temporal concurrent constraint programming which adds to tcc the capability of modeling asynchronous and nondeterministic timed behavior. We call this tcc extension the ntcc calculus. We also give a d ..."
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Cited by 87 (29 self)
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The tcc model is a formalism for reactive concurrent constraint programming. We present a model of temporal concurrent constraint programming which adds to tcc the capability of modeling asynchronous and nondeterministic timed behavior. We call this tcc extension the ntcc calculus. We also give a denotational semantics for the strongestpostcondition of ntcc processes and, based on this semantics, we develop a proof system for lineartemporal properties of these processes. The expressiveness of ntcc is illustrated by modeling cells, timed systems such as RCX controllers, multiagent systems such as the Predator /Prey game, and musical applications such as generation of rhythms patterns and controlled improvisation. 1
Temporal Description Logics: A Survey
, 2008
"... We survey temporal description logics that are based on standard temporal logics such as LTL and CTL. In particular, we concentrate on the computational complexity of the satisfiability problem and algorithms for deciding it. ..."
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Cited by 57 (11 self)
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We survey temporal description logics that are based on standard temporal logics such as LTL and CTL. In particular, we concentrate on the computational complexity of the satisfiability problem and algorithms for deciding it.
Specifying and reasoning about dynamic accesscontrol policies
 of Lecture Notes in Computer Science
, 2006
"... Abstract. Accesscontrol policies have grown from simple matrices to nontrivial specifications written in sophisticated languages. The increasing complexity of these policies demands correspondingly strong automated reasoning techniques for understanding and debugging them. The need for these techn ..."
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Cited by 52 (3 self)
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Abstract. Accesscontrol policies have grown from simple matrices to nontrivial specifications written in sophisticated languages. The increasing complexity of these policies demands correspondingly strong automated reasoning techniques for understanding and debugging them. The need for these techniques is even more pressing given the rich and dynamic nature of the environments in which these policies evaluate. We define a framework to represent the behavior of accesscontrol policies in a dynamic environment. We then specify several interesting, decidable analyses using firstorder temporal logic. Our work illustrates the subtle interplay between logical and statebased methods, particularly in the presence of threevalued policies. We also define a notion of policy equivalence that is especially useful for modular reasoning. 1
Monodic fragments of firstorder temporal logics: 20002001 A.D.
"... The aim of this paper is to summarize and analyze some results obtained in 20002001 about decidable and undecidable fragments of various firstorder temporal logics, give some applications in the field of knowledge representation and reasoning, and attract the attention of the `temporal community&a ..."
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Cited by 49 (8 self)
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The aim of this paper is to summarize and analyze some results obtained in 20002001 about decidable and undecidable fragments of various firstorder temporal logics, give some applications in the field of knowledge representation and reasoning, and attract the attention of the `temporal community' to a number of interesting open problems.
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 39 (12 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 31 (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
Temporalising Tractable Description Logics
"... It is known that for temporal languages, such as firstorder LTL, reasoning about constant (timeindependent) relations is almost always undecidable. This applies to temporal description logics as well: constant binary relations together with general concept subsumptions in combinations of LTL and t ..."
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Cited by 28 (8 self)
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It is known that for temporal languages, such as firstorder LTL, reasoning about constant (timeindependent) relations is almost always undecidable. This applies to temporal description logics as well: constant binary relations together with general concept subsumptions in combinations of LTL and the basic description logic ALC cause undecidability. In this paper, we explore temporal extensions of two recently introduced families of ‘weak’ description logics known as DLLite and EL. Our results are twofold: temporalisations of even rather expressive variants of DLLite turn out to be decidable, while the temporalisation of EL with general concept subsumptions and constant relations is undecidable.
On the freeze quantifier in constraint LTL: decidability and complexity
 I & C
, 2005
"... Constraint LTL, a generalization of LTL over Presburger constraints, is often used as a formal language to specify the behavior of operational models with constraints. The freeze quantifier can be part of the language, as in some realtime logics, but this variablebinding mechanism is quite general ..."
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Cited by 28 (8 self)
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Constraint LTL, a generalization of LTL over Presburger constraints, is often used as a formal language to specify the behavior of operational models with constraints. The freeze quantifier can be part of the language, as in some realtime logics, but this variablebinding mechanism is quite general and ubiquitous in many logical languages (firstorder temporal logics, hybrid logics, logics for sequence diagrams, navigation logics, etc.). We show that Constraint LTL over the simple domain =# augmented with the freeze operator is undecidable which is a surprising result regarding the poor language for constraints (only equality tests). Many versions of freezefree Constraint LTL are decidable over domains with qualitative predicates and our undecidability result actually establishes # 1 completeness. On the positive side, we provide complexity results when the domain is finite (EXPSPACEcompleteness) or when the formulae are flat in a sense introduced in the paper. Our undecidability results are quite sharp (i.e. with restrictions on the number of variables) and all our complexity characterizations insure completeness with respect to some complexity class (mainly PSPACE and EXPSPACE).
On the Products of Linear Modal Logics
 JOURNAL OF LOGIC AND COMPUTATION
, 2001
"... We study twodimensional Cartesian products of modal logics determined by infinite or arbitrarily long finite linear orders and prove a general theorem showing that in many cases these products are undecidable, in particular, such are the squares of standard linear logics like K4:3, S4:3, GL:3, Grz: ..."
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Cited by 27 (10 self)
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We study twodimensional Cartesian products of modal logics determined by infinite or arbitrarily long finite linear orders and prove a general theorem showing that in many cases these products are undecidable, in particular, such are the squares of standard linear logics like K4:3, S4:3, GL:3, Grz:3, or the logic determined by the Cartesian square of any infinite linear order. This theorem solves a number of open problems of Gabbay and Shehtman [7]. We also prove a sufficient condition for such products to be not recursively enumerable and give a simple axiomatisation for the square K4:3 K4:3 of the minimal liner logic using nonstructural Gabbaytype inference rules.
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 25 (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.