ML-1996-07: Decidable Theories of $\omega$-Layered Metric Temporal Structures

ML-1996-07: Montanari, Angelo and Peron, Adriano and Policriti, Alberto (1996) Decidable Theories of $\omega$-Layered Metric Temporal Structures. [Report]

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Abstract

This paper focuses on decidability problems for metric and layered temporal logics which allow one to model time granularity in various contexts. The decidability of pure metric (non­granular) fragments and of metric temporal logics endowed with finitely many layers has been already proved by reduction to the decidability problem of the well­known theory S1S. In the present work, we prove the decidability of both the theory of metric temporal structures provided with an infinite number of arbitrarily coarse temporal layers and the theory of metric temporal structures provided with an infinite number of arbitrarily fine temporal layers. The proof for the first theory is obtained by reduction to the decidability problem of an extension of S1S which is proved to be the logical counterpart of the class of \omega­languages accepted by systolic tree automata. The proof for the second one is done through the reduction to the monadic second­order decidable theory of k successors SkS.

Item Type: Report
Report Nr: ML-1996-07
Series Name: Mathematical Logic and Foundations (ML)
Year: 1996
Date Deposited: 12 Oct 2016 14:40
Last Modified: 12 Oct 2016 14:40
URI: https://eprints.illc.uva.nl/id/eprint/1376

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