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Article Dans Une Revue Logica Universalis Année : 2007

Cut-free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics

Résumé

The paper presents a method for transforming a given sound and complete n-sequent proof system into an equivalent sound and complete system of ordinary sequents. The method is applicable to a large, central class of (generalized) finite-valued logics with the language satisfying a certain minimal expressiveness condition. The expressiveness condition decrees that the truth-value of any formula φ must be identifiable by determining whether certain formulas uniformly constructed from φ have designated values or not. The transformation preserves the general structure of proofs in the original calculus in a way ensuring preservation of the weak cut elimination theorem under the transformation. The described transformation metod is illustrated on several concrete examples of many-valued logics, including a new application to information sources logics.
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Dates et versions

hal-03466419 , version 1 (05-12-2021)

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Arnon Avron, Jonathan Ben-Naim, Beata Konikowska. Cut-free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics. Logica Universalis, 2007, 1, pp.41-70. ⟨10.1007/s11787-006-0003-6⟩. ⟨hal-03466419⟩
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