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Hypersequent Calculi for Lewis’ Conditional Logics with Uniformity and Reflexivity

  • Marianna Girlando
  • Björn Lellmann
  • Nicola Olivetti
  • Gian Luca Pozzato
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10501)

Abstract

We present the first internal calculi for Lewis’ conditional logics characterized by uniformity and reflexivity, including non-standard internal hypersequent calculi for a number of extensions of the logic \(\mathbb {V}\mathbb {T}\mathbb {U}\). These calculi allow for syntactic proofs of cut elimination and known connections to \(\mathsf {S5}\). We then introduce standard internal hypersequent calculi for all these logics, in which sequents are enriched by additional structures to encode plausibility formulas as well as diamond formulas. These calculi provide both a decision procedure for the respective logics and constructive countermodel extraction from a failed proof search attempt.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

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

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