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

The gamma-admissibility is one of the most important problems in the realm of relevant logics. To prove the gamma-admissibility, either the method of normal models or the method using metavaluations may be employed. The gamma-admissibility of a wide class of relevant modal logics has been discussed in Part I based on a former method, but the gamma-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 gamma is admissible for relevant modal logics with restricted Sahlqvist axioms in terms of the method using metavaluations.