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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Acknowledgements
The authors acknowledge the support from the Italian GNCS project Logics, automata, and games for auto-adaptive systems. In addition, Dario Della Monica and Aniello Murano acknowledge the support from the POR Campania project Strategic reasoning for multi-agent systems.
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Della Monica, D., Montanari, A., Murano, A., Sala, P. (2016). Prompt Interval Temporal Logic. In: Michael, L., Kakas, A. (eds) Logics in Artificial Intelligence. JELIA 2016. Lecture Notes in Computer Science(), vol 10021. Springer, Cham. https://doi.org/10.1007/978-3-319-48758-8_14
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DOI: https://doi.org/10.1007/978-3-319-48758-8_14
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