Abstract
The logic \({\mathbb V}\) 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 \(\mathbb{V}\).
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Olivetti, N., Pozzato, G.L. (2015). A Standard Internal Calculus for Lewis’ Counterfactual Logics. In: De Nivelle, H. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2015. Lecture Notes in Computer Science(), vol 9323. Springer, Cham. https://doi.org/10.1007/978-3-319-24312-2_19
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DOI: https://doi.org/10.1007/978-3-319-24312-2_19
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