Uniform labelled calculi for conditional and counterfactual logics

Marianna Girlando (1) , Sara Negri (2) , Giorgio Sbardolini (3)

1 LIRICA - Logique, Interaction, Raisonnement et Inférence, Complexité, Algèbre
2 Helsingin yliopisto = Helsingfors universitet = University of Helsinki
3 OSU - Ohio State University [Columbus]

Lewis's counterfactual logics are a class of conditional logics that are defined as extensions of classical propositional logic with a two-place modal operator expressing conditionality. Labelled proof systems are proposed here that capture in a modular way Burgess's preferential conditional logic PCL, Lewis's counterfactual logic V, and their extensions. The calculi are based on preferential models, a uniform semantics for conditional logics introduced by Lewis. The calculi are analytic, and their completeness is proved by means of countermodel construction. Due to termination in root-first proof search, the calculi also provide a decision procedure for the logics.

Domaines: Logique en informatique [cs.LO]

Marianna Girlando, Sara Negri, Giorgio Sbardolini. Uniform labelled calculi for conditional and counterfactual logics. WoLLIC 2019, Jul 2019, Utrecht, Netherlands. ⟨hal-02330313⟩