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Metacompleteness of Substructural Logics

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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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  1. University Evaluation Center, Headquarters for Strategy and Planning, Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku, Niigata City, 950-2181, Japan

    Takahiro Seki

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  1. Takahiro Seki
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Correspondence to Takahiro Seki.

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Seki, T. Metacompleteness of Substructural Logics. Stud Logica 100, 1175–1199 (2012). https://doi.org/10.1007/s11225-012-9458-z

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  • DOI: https://doi.org/10.1007/s11225-012-9458-z

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