Abstract
Minimal entailment is the semantical counterpart of Circumscription and Closed World Assumption. In this paper we show that it is possible to formalize minimal entailment at the propositional level, using standard deduction methods. Firstly we present a tableau procedure which is a natural reformulation of Smullyan's Analytic Tableaux. Then we introduce the sequent calculus MLK which is an extension of Gentzen's LK calculus. We prove that both are sound and complete formalizations of minimal entailment. Various extensions of the proposed methods are also discussed.
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Olivetti, N. Tableaux and sequent calculus for minimal entailment. J Autom Reasoning 9, 99–139 (1992). https://doi.org/10.1007/BF00247828
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DOI: https://doi.org/10.1007/BF00247828