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The γ-admissibility of Relevant Modal Logics II — The Method using Metavaluations

Abstract

The γ-admissibility is one of the most important problems in the realm of relevant logics. To prove the γ-admissibility, either the method of normal models or the method using metavaluations may be employed. The γ-admissibility of a wide class of relevant modal logics has been discussed in Part I based on a former method, but the γ-admissibility based on metavaluations has not hitherto been fully considered. Sahlqvist axioms are well known as a means of expressing generalized forms of formulas with modal operators. This paper shows that γ is admissible for relevant modal logics with restricted Sahlqvist axioms in terms of the method using metavaluations.

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Correspondence to Takahiro Seki.

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Seki, T. The γ-admissibility of Relevant Modal Logics II — The Method using Metavaluations. Stud Logica 97, 351–383 (2011). https://doi.org/10.1007/s11225-011-9315-5

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Keywords

  • γ-admissibility
  • relevant modal logic
  • metavaluation
  • Sahlqvist axiom