Gentzen semantics for de Morgan lattice logic1

Bulletin of the Section of Logic 15 (1):96-102 (1986)
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Abstract

DeMorgan lattice logic is the consecution version of Anderson/Belnap’s calculus of First Degree Entailments [1]. Theorems of DML are of the form Γ ` A, where Γ is a non-empty set of formulae. Let Γ = {A1, . . . , An}, then Γ ` A is a theorem of DML if and only if A1& . . . &An → A is a theorem of F DE. The Gentzenization of DML offered in this paper, LDML, derives from the worlds semantics for F DE, first presented in [3]. It is for this reason that LDML may be called a “Gentzen semantics” for DML

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André Fuhrmann
Goethe University Frankfurt

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