Studia Logica

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

Natural Deduction Calculi and Sequent Calculi for Counterfactual Logics

  • Francesca Poggiolesi


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.


Natural deduction calculus Sequent calculus Normalization Counterfactual logics 


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© 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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