Standard Sequent Calculi for Lewis’ Logics of Counterfactuals

  • Marianna Girlando
  • Björn Lellmann
  • Nicola Olivetti
  • Gian Luca Pozzato
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10021)

Abstract

We present new sequent calculi for Lewis’ logics of counterfactuals. The calculi are based on Lewis’ connective of comparative plausibility and modularly capture almost all logics of Lewis’ family. Our calculi are standard, in the sense that each connective is handled by a finite number of rules with a fixed and finite number of premises; internal, meaning that a sequent denotes a formula in the language, and analytical. We present two equivalent versions of the calculi: in the first one, the calculi comprise simple rules; we show that for the basic case of logic \(\mathbb {V}\), the calculus allows for syntactic cut-elimination, a fundamental proof-theoretical property. In the second version, the calculi comprise invertible rules, they allow for terminating proof search and semantical completeness. We finally show that our calculi can simulate the only internal (non-standard) sequent calculi previously known for these logics.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Marianna Girlando
    • 1
  • Björn Lellmann
    • 2
  • Nicola Olivetti
    • 1
  • Gian Luca Pozzato
    • 3
  1. 1.Aix Marseille Univ, CNRS, ENSAM, Université de Toulon, LSIS UMR 7296MarseilleFrance
  2. 2.Technische Universität WienViennaAustria
  3. 3.Dipartimento di InformaticaUniversitá di TorinoTurinItaly

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