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

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.
Keywords Metacompleteness  Substructural logics  Disjunction property  Existence property  Admissible rules
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DOI 10.1007/s11225-012-9458-z
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Relevance Logic.Michael Dunn & Greg Restall - 2002 - In D. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic. Kluwer Academic Publishers.
Concerning Formulas of the Types a →B ∨C, a →(Ex)B(X).Ronald Harrop - 1960 - Journal of Symbolic Logic 25 (1):27-32.

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