Natural deduction calculi and sequent calculi for counterfactual logics

Francesca Poggiolesi (1)

1 IHPST - Institut d'Histoire et de Philosophie des Sciences et des Techniques

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.

Mots clés: Proof Theory; Counterfatcual logics

Domaines: Philosophie

Francesca Poggiolesi. Natural deduction calculi and sequent calculi for counterfactual logics. Studia Logica, 2016, 104 (5), pp.1003-1036. ⟨10.1007/s11225-016-9662-3⟩. ⟨hal-01271556⟩