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On the Expressive Equivalence of TPTL in the Pointwise and Continuous Semantics

Authors Raveendra Holla, Nabarun Deka, Deepak D'Souza

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Author Details

Raveendra Holla
  • Citrix Systems India Pvt. Ltd., Bangalore, India
Nabarun Deka
  • Indian Institute of Science Bangalore, India
Deepak D'Souza
  • Indian Institute of Science Bangalore, India

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Raveendra Holla, Nabarun Deka, and Deepak D'Souza. On the Expressive Equivalence of TPTL in the Pointwise and Continuous Semantics. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 45:1-45:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.FSTTCS.2021.45

Abstract

We consider a first-order logic with linear constraints interpreted in a pointwise and continuous manner over timed words. We show that the two interpretations of this logic coincide in terms of expressiveness, via an effective transformation of sentences from one logic to the other. As a consequence it follows that the pointwise and continuous semantics of the logic TPTL with the since operator also coincide. Along the way we exhibit a useful normal form for sentences in these logics.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
Keywords
  • Real-Time Logics
  • First-Order Logics

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