One-Pass and Tree-Shaped Tableau Systems for TPTL and TPTLb+Past

Luca Geatti, Nicola Gigante, Angelo Montanari, Mark Reynolds

Research output: Chapter in Book/Conference paperConference paper

1 Citation (Scopus)
229 Downloads (Pure)

Abstract

In this paper, we propose a novel one-pass and tree-shaped tableau method for Timed Propositional Temporal Logic and for a bounded variant of its extension with past operators. Timed Propositional Temporal Logic (TPTL) is a real-time temporal logic, with an EXPSPACE-complete satisfiability problem, which has been successfully applied to the verification of real-time systems. In contrast to LTL, adding past operators to TPTL makes the satisfiability problem for the resulting logic (TPTL+P) non-elementary. In this paper, we devise a one-pass and tree-shaped tableau for both TPTL and bounded TPTL+P (TPTLb+P), a syntactic restriction introduced to encode timeline-based planning problems, which recovers the EXPSPACE-complete complexity. The tableau systems for TPTL and TPTLb+P are presented in a unified way, being very similar to each other, providing a common skeleton that is then specialised to each logic. In doing that, we characterise the semantics of TPTLb+P in terms of a purely syntactic fragment of TPTL+P, giving a translation that embeds the former into the latter. Soundness and completeness of the system are proved fully. In particular, we give a greatly simplified model-theoretic completeness proof, which sidesteps the complex combinatorial argument used by known proofs for the one-pass and tree-shaped tableau systems for LTL and LTL+P.

Original languageEnglish
Title of host publicationProceedings Ninth International Symposium on Games, Automata, Logics, and Formal Verification, GandALF 2018, Saarbrucken, Germany, 26-28th September 2018.
EditorsAndrea Orlandini, Martin Zimmermann
PublisherOpen Publishing Association
Pages176-190
Publication statusPublished - 7 Sep 2018
EventNinth International Symposium on Games, Automata, Logics, and Formal Verification - Saarbrücken, Germany
Duration: 26 Sep 201828 Sep 2018

Conference

ConferenceNinth International Symposium on Games, Automata, Logics, and Formal Verification
CountryGermany
CitySaarbrücken
Period26/09/1828/09/18

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