Metacompleteness of Substructural Logics

Studia Logica 100 (6):1175-1199 (2012)
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Abstract

Metacompleteness is used to prove properties such as the disjunction property and the existence property in the area of relevant logics. On the other hand, the disjunction property of several basic propositional substructural logics over FL has been proved using the cut elimination theorem of sequent calculi and algebraic characterization. The present paper shows that Meyer’s metavaluational technique and Slaney’s metavaluational technique can be applied to basic predicate intuitionistic substructural logics and basic predicate involutive substructural logics, respectively. As a corollary of metacompleteness, the disjunction property, the existence property, and the admissibility of certain rules in such logics can be proved.

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References found in this work

Relevance Logic.Michael Dunn & Greg Restall - 1983 - In Dov M. Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic. Dordrecht, Netherland: Kluwer Academic Publishers.
Reduced models for relevant logics without ${\rm WI}$.John K. Slaney - 1987 - Notre Dame Journal of Formal Logic 28 (3):395-407.

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