The logic V is the basic logic of counterfactuals in the family of Lewis' systems. It is characterized by the whole class of so-called sphere models. We propose a new sequent calculus for this logic. Our calculus takes as primitive Lewis' connective of comparative plausibility <= : a formula A <= B intuitively means that A is at least as plausible as B. Our calculus is standard in the sense that each connective is handled by a finite number of rules with a fixed and finite number of premises. Moreover our calculus is "internal", in the sense that each sequent can be directly translated into a formula of the language. We show that the calculus provides an optimal decision procedure for the logic V.

### A standard and internal calculus for Lewis counterfactual logics

#### Abstract

The logic V is the basic logic of counterfactuals in the family of Lewis' systems. It is characterized by the whole class of so-called sphere models. We propose a new sequent calculus for this logic. Our calculus takes as primitive Lewis' connective of comparative plausibility <= : a formula A <= B intuitively means that A is at least as plausible as B. Our calculus is standard in the sense that each connective is handled by a finite number of rules with a fixed and finite number of premises. Moreover our calculus is "internal", in the sense that each sequent can be directly translated into a formula of the language. We show that the calculus provides an optimal decision procedure for the logic V.
##### Scheda breve Scheda completa Scheda completa (DC)
2015
Proceedings of the 22nd Conference on Automated Reasoning with Analytic Tableaux and Related Methods (Tableaux 2015)
Wrocaw, POLAND
21 September 2015 through 24 September 2015
AUTOMATED REASONING WITH ANALYTIC TABLEAUX AND RELATED METHODS (TABLEAUX 2015)
SPRINGER-VERLAG
9323
270
286
978-3-319-24312-2
Olivetti, Nicola; Pozzato, Gian Luca
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2318/1640076`