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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 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
The Logic of Time Representation
, 1987
"... This investigation concerns representations of time by means of intervals, stemming from work of Allen [All83] and van Benthem [vBen83]. Allen described an Interval Calculus of thirteen binary relations on convex intervals over a linear order (the real numbers). He gave a practical algorithm for che ..."
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Cited by 29 (1 self)
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This investigation concerns representations of time by means of intervals, stemming from work of Allen [All83] and van Benthem [vBen83]. Allen described an Interval Calculus of thirteen binary relations on convex intervals over a linear order (the real numbers). He gave a practical algorithm for checking the consistency of a subclass of Boolean constraints. First, we describe a completeness theorem for Allen's calculus, in its corresponding formulation as a firstorder theory LM . LM is countably categorical, and axiomatises the complete theory of intervals over a dense unbounded linear order. Its only countable model up to isomorphism is the nontrivial intervals over the rational numbers. Algorithms are given for quantiferelimination, consistency checking, and satisfaction of arbitrary firstorder formulas in the Interval Calculus. A natural countable model of the calculus is presented, the TUS , in which clock and calendartime may be represented in a straightforward way. Allen an...
Proving Entailment Between Conceptual State Specifications (Extended Abstract)
 Theoretical Computer Science
, 1988
"... ) Eugene W. Stark y Abstract The lack of expressive power of temporal logic as a specification language can be compensated to a certain extent by the introduction of powerful, highlevel temporal operators, which are difficult to understand and reason about. A more natural way to increase the expr ..."
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) Eugene W. Stark y Abstract The lack of expressive power of temporal logic as a specification language can be compensated to a certain extent by the introduction of powerful, highlevel temporal operators, which are difficult to understand and reason about. A more natural way to increase the expressive power of a temporal specification language is by introducing conceptual state variables, which are auxiliary (unimplemented) variables whose values serve as an abstract representation of the internal state of the process being specified. The kind of specifications resulting from the latter approach are called conceptual state specifications. This paper considers a central problem in reasoning about conceptual state specifications: the problem of proving entailment between specifications. A technique, based on the notion of simulation between machines, is shown to be sound for proving entailment. A kind of completeness result can also be shown, if specifications are assumed to satisf...
Temporal Logic with Past is Exponentially More Succinct
, 2003
"... We positively answer the old question whether temporal logic with past is more succinct than purefuture temporal logic. Surprisingly, the proof is quite simple and elementary, although the question has been open for twenty years. ..."
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Cited by 13 (0 self)
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We positively answer the old question whether temporal logic with past is more succinct than purefuture temporal logic. Surprisingly, the proof is quite simple and elementary, although the question has been open for twenty years.
A Tableau Calculus For FirstOrder Branching Time Logic
 Intl. Conf. on Formal and Applied Practical Reasoning, FAPR'96, Springer LNCS 1085
, 1996
"... Abstract. Tableaubased proof systems have been designed for many logics extending classical rstorder logic. This paper proposes a sound tableau calculus for temporal logics of the rstorder CTLfamily. Until now, a tableau calculus has only been presented for the propositional version of CTL. The ..."
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Abstract. Tableaubased proof systems have been designed for many logics extending classical rstorder logic. This paper proposes a sound tableau calculus for temporal logics of the rstorder CTLfamily. Until now, a tableau calculus has only been presented for the propositional version of CTL. The calculus considered operates with pre xed formulas and may be regarded as an instance of a labelled deductive system. The pre xes allow an explicit partial description of states and paths of a potential Kripke counter model in the tableau. It is possible in particular to represent path segments of nite but arbitrary length which are needed to process reachability formulas. Furthermore, we show that by using pre xed formulas and explicit representation of paths it becomes possible to express and process fairness properties without having to resort to full CTL. The approach is suitable for use in interactive proofsystems. 1
On Axiomatizations for Propositional Logics of Programs
, 1988
"... this paper, we focus attention on a propositional program logic, namely Propositional Dynamic Logic or PDL in short ..."
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Cited by 1 (1 self)
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this paper, we focus attention on a propositional program logic, namely Propositional Dynamic Logic or PDL in short
Propositional Scopes in Linear Temporal Logic
"... Abstract — In this paper, we address the problem of specifying a property in LTL over a subset of the states of a system under test, ignoring the rest of the states. A modern LTL semantics that applies for both finite and infinite traces is considered. We introduce specialized operators (syntax and ..."
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Abstract — In this paper, we address the problem of specifying a property in LTL over a subset of the states of a system under test, ignoring the rest of the states. A modern LTL semantics that applies for both finite and infinite traces is considered. We introduce specialized operators (syntax and semantic) that help specifying properties over propositional scopes, where each scope constitute a subset of states that satisfy a propositional logic formula. These operators assist the user in specifying the properties more easily and intuitively. I.
BTL2 and expressive completeness for ECTL+
, 2000
"... We show that ECTL , the classical extension of CTL with fairness properties, is expressively equivalent to BTL2 . BTL2 is the branching time logic with abritrary quanti cation over paths, and where path formulae are restricted to quanti er depth rstorder formulae in the monadic logic of o ..."
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We show that ECTL , the classical extension of CTL with fairness properties, is expressively equivalent to BTL2 . BTL2 is the branching time logic with abritrary quanti cation over paths, and where path formulae are restricted to quanti er depth rstorder formulae in the monadic logic of order. This result, linking ECTL to a natural fragment of the monadic logic of order, provides a characterization that other branching time logics, e.g. CTL, lack.
BTL2 and the expressive power of ECTL+
, 2006
"... We show that ECTL +, the classical extension of CTL with fairness properties, is expressively equivalent to BTL2, a natural fragment of the monadic logic of order. BTL2 is the branchingtime logic with arbitrary quantification over paths, and where path formulae are restricted to quantifier depth ..."
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We show that ECTL +, the classical extension of CTL with fairness properties, is expressively equivalent to BTL2, a natural fragment of the monadic logic of order. BTL2 is the branchingtime logic with arbitrary quantification over paths, and where path formulae are restricted to quantifier depth 2 firstorder formulae in the monadic logic of order. This result, linking ECTL + to a natural fragment of the monadic logic of order, provides a characterization that other branchingtime logics, e.g., CTL, lack. We then go on to show that ECTL + and BTL2 are not finitely based (i.e., they cannot be defined by a finite set of temporal modalities) and that their modelchecking problems are of the same complexity.