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, so that a conditional A ⇒ B can be defined as A is impossible or A ∧ ¬B is less plausible than A. As a difference with previous attempts, 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. The peculiarity of our calculus is that sequents contain a special kind of structures, called blocks, which encode a finite combination of ≼. We show that the calculus is terminating, whence it provides a decision procedure for the logic V.

### A natural sequent calculus for Lewis logic of counterfactuals

#### 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, so that a conditional A ⇒ B can be defined as A is impossible or A ∧ ¬B is less plausible than A. As a difference with previous attempts, 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. The peculiarity of our calculus is that sequents contain a special kind of structures, called blocks, which encode a finite combination of ≼. We show that the calculus is terminating, whence it provides a decision procedure for the logic V.
##### Scheda breve Scheda completa Scheda completa (DC) 2015
30° Convegno Italiano di Logica Computazionale
Genova
1-3 luglio 2015
Proceedings of the 30th Italian Conference on Computational Logic
CEUR Workshop Proceedings
1459
13
18
http://ceur-ws.org/Vol-1459/paper14.pdf
conditional logics, sequent calculi, nonmonotonic reasoning, counterfactual reasoning
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/2318/1526133`
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