Logic and computer science communities have traditionally followed a different approach to the problem of representing and reasoning about time and states. Research in logic resulted in a family of (metric) tense logics that take time as a primitive notion and definite (timed) states as sets of atomic propositions which are true at given instants, while research in computer science concentrated on the so-called (real-time) temporal logics of programs that take state as a primitive notion, and define time as an attribute of states. In this paper, we provide a unifying framework within which the two approaches can be reconciled. Our main tools are metric and layered temporal logics originally proposed to model time granularity in various contexts. In such a framework, states and time-instants can be uniformly referred to as elements of a (decidable) theory of omega-layered metric temporal structures. Furthermore, we show that the theory of timed state sequences, underlying real-time logics, is naturally recovered as an abstraction of such a theory.

The taming (timing) of the states

MONTANARI, Angelo;PERON, Adriano;POLICRITI, Alberto
2000-01-01

Abstract

Logic and computer science communities have traditionally followed a different approach to the problem of representing and reasoning about time and states. Research in logic resulted in a family of (metric) tense logics that take time as a primitive notion and definite (timed) states as sets of atomic propositions which are true at given instants, while research in computer science concentrated on the so-called (real-time) temporal logics of programs that take state as a primitive notion, and define time as an attribute of states. In this paper, we provide a unifying framework within which the two approaches can be reconciled. Our main tools are metric and layered temporal logics originally proposed to model time granularity in various contexts. In such a framework, states and time-instants can be uniformly referred to as elements of a (decidable) theory of omega-layered metric temporal structures. Furthermore, we show that the theory of timed state sequences, underlying real-time logics, is naturally recovered as an abstraction of such a theory.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/722553
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