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A Sequent Calculus for Preferential Conditional Logic Based on Neighbourhood Semantics

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9323))

Abstract

The basic preferential conditional logic PCL, initially proposed by Burgess, finds an interest in the formalisation of both counterfactual and plausible reasoning, since it is at the same time more general than Lewis’ systems for counterfactuals and it contains as a fragment the KLM preferential logic P for default reasoning. This logic is characterised by Kripke models equipped with a ternary relational semantics that represents a comparative similarity/normality assessment between worlds, relativised to each world. It is first shown that its semantics can be equivalently specified in terms of neighbourhood models. On the basis of this alternative semantics, a new labelled calculus is given that makes use of both world and neighbourhood labels. It is shown that the calculus enjoys syntactic cut elimination and that, by adding suitable termination conditions, it provides a decision procedure.

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Author information

Authors and Affiliations

  1. Department of Philosophy, University of Helsinki, Helsinki, Finland

    Sara Negri

  2. Aix Marseille University, CNRS, ENSAM, Toulon University, LSIS UMR 7296, 13397, Marseille, France

    Nicola Olivetti

Authors
  1. Sara Negri
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  2. Nicola Olivetti
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Corresponding author

Correspondence to Sara Negri .

Editor information

Editors and Affiliations

  1. Uniwersytet Wrocławski, Wrocław, Poland

    Hans De Nivelle

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Negri, S., Olivetti, N. (2015). A Sequent Calculus for Preferential Conditional Logic Based on Neighbourhood Semantics. In: De Nivelle, H. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2015. Lecture Notes in Computer Science(), vol 9323. Springer, Cham. https://doi.org/10.1007/978-3-319-24312-2_9

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  • DOI: https://doi.org/10.1007/978-3-319-24312-2_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24311-5

  • Online ISBN: 978-3-319-24312-2

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