Standard Sequent Calculi for Lewis' Logics of Counterfactuals

Marianna Girlando (1, 2) , Björn Lellmann (3) , Nicola Olivetti (1, 2) , Gian Luca Pozzato (4)

1 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
2 LIRICA - Logique, Interaction, Raisonnement et Inférence, Complexité, Algèbre
3 TU Wien - Vienna University of Technology = Technische Universität Wien
4 Dipartimento di Informatica [Torino]

We present new sequent calculi for Lewis' logics of coun-terfactuals. The calculi are based on Lewis' connective of comparative plausibility and modularly capture almost all logics of Lewis' family. Our calculi are standard, in the sense that each connective is handled by a finite number of rules with a fixed and finite number of premises; internal, meaning that a sequent denotes a formula in the language, and analytical. We present two equivalent versions of the calculi: in the first one, the calculi comprise simple rules; we show that for the basic case of logic V, the calculus allows for syntactic cut-elimination, a fundamental proof-theoretical property. In the second version, the calculi comprise invertible rules, they allow for terminating proof search and semantical completeness. We finally show that our calculi can simulate the only internal (non-standard) sequent calculi previously known for these logics.

Domaines: Informatique [cs]

Marianna Girlando, Björn Lellmann, Nicola Olivetti, Gian Luca Pozzato. Standard Sequent Calculi for Lewis' Logics of Counterfactuals. JELIA 2016, Nov 2016, Larnaca, Cyprus. ⟨hal-01794375⟩