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2016 | OriginalPaper | Chapter

Prompt Interval Temporal Logic

Authors : Dario Della Monica, Angelo Montanari, Aniello Murano, Pietro Sala

Published in: Logics in Artificial Intelligence

Publisher: Springer International Publishing

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Abstract

Interval temporal logics are expressive formalisms for temporal representation and reasoning, which use time intervals as primitive temporal entities. They have been extensively studied for the past two decades and successfully applied in AI and computer science. Unfortunately, they lack the ability of expressing promptness conditions, as it happens with the commonly-used temporal logics, e.g., LTL: whenever we deal with a liveness request, such as “something good eventually happens”, there is no way to impose a bound on the delay with which it is fulfilled. In the last years, such an issue has been addressed in automata theory, game theory, and temporal logic. In this paper, we approach it in the interval temporal logic setting. First, we introduce PROMPT- PNL, a prompt extension of the well-studied interval temporal logic PNL, and we prove the undecidability of its satisfiability problem; then, we show how to recover decidability (NEXPTIME-completeness) by imposing a natural syntactic restriction on it.

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Title: Prompt Interval Temporal Logic
Authors: Dario Della Monica
Angelo Montanari
Aniello Murano
Pietro Sala
Publisher: Springer International Publishing
Book: Logics in Artificial Intelligence
Print ISBN: 978-3-319-48757-1

Electronic ISBN: 978-3-319-48758-8

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-3-319-48758-8_14

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