A Cut-Free and Invariant-Free Sequent Calculus for PLTL

  • Joxe Gaintzarain
  • Montserrat Hermo
  • Paqui Lucio
  • Marisa Navarro
  • Fernando Orejas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4646)

Abstract

Sequent calculi usually provide a general deductive setting that uniformly embeds other proof-theoretical approaches, such as tableaux methods, resolution techniques, goal-directed proofs, etc. Unfortunately, in temporal logic, existing sequent calculi make use of a kind of inference rules that prevent the effective mechanization of temporal deduction in the general setting. In particular, temporal sequent calculi either need some form of cut, or they make use of invariants, or they include infinitary rules. This is the case even for the simplest kind of temporal logic, propositional linear temporal logic (PLTL). In this paper, we provide a complete finitary sequent calculus for PLTL, called \(\mathcal{FC}\), that not only is cut-free but also invariant-free. In particular, we introduce new rules which provide a new style of temporal deduction. We give a detailed proof of completeness.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Joxe Gaintzarain
    • 1
  • Montserrat Hermo
    • 1
  • Paqui Lucio
    • 1
  • Marisa Navarro
    • 1
  • Fernando Orejas
    • 2
  1. 1.Dpto de Lenguajes y Sistemas Informáticos, Universidad del País Vasco, 20080-San SebastiánSpain
  2. 2.Dpto de Lenguajes y Sistemas Informáticos, Universidad Politécnica de Catalunya, 08034-BarcelonaSpain

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