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Decidability for Priorean Linear Time Using a Fixed-Point Labelled Calculus

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5607))

Abstract

A labelled sequent calculus is proposed for Priorean linear time logic, the rules of which reflect a natural closure algorithm derived from the fixed-point properties of the temporal operators. All the rules of the system are finitary, but proofs may contain infinite branches. Soundness and completeness of the calculus are stated with respect to a notion of provability based on a condition on derivation trees: A sequent is provable if and only if no branch leads to a ‘fulfilling sequent,’ the syntactical counterpart of a countermodel for an invalid sequent. Decidability is proved through a terminating proof search procedure, with an exponential bound to the branches of derivation trees for valid sequents, calculated on the length of the characteristic temporal formula of the endsequent.

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Author information

Authors and Affiliations

  1. Dept. of Electronics and Information, Polytechnic of Milan,  

    Bianca Boretti

  2. Dept. of Philosophy, University of Helsinki,  

    Sara Negri

Authors
  1. Bianca Boretti
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  2. Sara Negri
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Oslo, Blindern, P.O. Box 1080, 0316, Oslo, Norway

    Martin Giese  & Arild Waaler  & 

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Boretti, B., Negri, S. (2009). Decidability for Priorean Linear Time Using a Fixed-Point Labelled Calculus. In: Giese, M., Waaler, A. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2009. Lecture Notes in Computer Science(), vol 5607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02716-1_9

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  • DOI: https://doi.org/10.1007/978-3-642-02716-1_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02715-4

  • Online ISBN: 978-3-642-02716-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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