We present new sequent calculi for Lewis' logics of counterfactuals. 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.

### Standard Sequent Calculi for Lewis' Logics of Counterfactuals

#### Abstract

We present new sequent calculi for Lewis' logics of counterfactuals. 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.
##### Scheda breve Scheda completa Scheda completa (DC) 2016
JELIA 2016 - 15th European Conference On Logics In Artificial Intelligence
Larnaca; Cyprus
9 November 2016 through 11 November 2016
Proceedings of JELIA 2016 - 15th European Conference On Logics In Artificial Intelligence
SPRINGER INT PUBLISHING AG
10021
272
287
978-3-319-48758-8
Marianna, Girlando; Bjoern, Lellmann; Nicola, Olivetti; Gian, Luca Pozzato
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2318/1640054`
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