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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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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
Formal Methods for the Specification and Design of RealTime Safety Critical Systems
, 1992
"... Safety critical computers increasingly a#ect nearly every aspect of our lives. Computers control the planes we #y on, monitor our health in hospitals and do our work in hazardous environments. Computers with software de#ciencies that fail to meet stringent timing constraints have resulted in cat ..."
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Safety critical computers increasingly a#ect nearly every aspect of our lives. Computers control the planes we #y on, monitor our health in hospitals and do our work in hazardous environments. Computers with software de#ciencies that fail to meet stringent timing constraints have resulted in catastrophic failures. This paper surveys formal methods for specifying, designing and verifying realtime systems, so as to improve their safety and reliability. # To appear in Journal of Systems and Software,Vol. 18, Number 1, pages 33#60, April 1992. Jonathan Ostro# is with the Department of Computer Science, York University 4700 Keele Street, North York, Ontario, Canada, M3J 1P3. This work is supported by the Natural Sciences and Engineering Research Council of Canada. 1 CONTENTS 2 Contents 1 Introduction 3 2 De#ning the terms 6 2.1 Major issues that formal theories must address ::::::: 13 3 RealTime Programming Languages 14 4 Structured Methods and#or Graphical Languages 15 4.1 Str...
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 34 (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...
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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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.
Proving Entailment Between Conceptual State Specifications (Extended Abstract)
 THEORETICAL COMPUTER SCIENCE
, 1988
"... 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 spe ..."
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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...
An Axiomatic Semantics of Concurrent Programming Languages
, 1984
"... this paper, I present a new compositional, truly axiomatic semantics for concurrent programming languages. It is based upon temporal logic, but employs five fundamental ideas beyond those found in most temporal logic methods: ..."
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this paper, I present a new compositional, truly axiomatic semantics for concurrent programming languages. It is based upon temporal logic, but employs five fundamental ideas beyond those found in most temporal logic methods:
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
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.