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Natural Deduction Calculi and Sequent Calculi for Counterfactual Logics

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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.

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

    Francesca Poggiolesi

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  1. Francesca Poggiolesi
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Correspondence to Francesca Poggiolesi.

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Poggiolesi, F. Natural Deduction Calculi and Sequent Calculi for Counterfactual Logics. Stud Logica 104, 1003–1036 (2016). https://doi.org/10.1007/s11225-016-9662-3

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  • DOI: https://doi.org/10.1007/s11225-016-9662-3

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