Studia Logica

, Volume 104, Issue 5, pp 1003–1036 | Cite as

Natural Deduction Calculi and Sequent Calculi for Counterfactual Logics

Article

Abstract

In this paper we present labelled sequent calculi and labelled natural deduction calculi for the counterfactual logics CK + {ID, MP}. As for the sequent calculi we prove, in a semantic manner, that the cut-rule is admissible. As for the natural deduction calculi we prove, in a purely syntactic way, the normalization theorem. Finally, we demonstrate that both calculi are sound and complete with respect to Nute semantics [12] and that the natural deduction calculi can be effectively transformed into the sequent calculi.

Keywords

Natural deduction calculus Sequent calculus Normalization Counterfactual logics 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Université Paris 1 Panthéon-Sorbonne, CNRS, ENS, UMR 8590 IHPST - Institut d’Histoire et de Philosophie des Sciences et des TechniquesParisFrance

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