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

Studia Logica 97 (3):351-383 (2011)
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Abstract

The?-admissibility is one of the most important problems in the realm of relevant logics. To prove the 7-admissibility, either the method of normal models or the method using metavaluations may be employed. The?-admissibility of a wide class of relevant modal logics has been discussed in Part I based on a former method, but the?-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? is admissible for relevant modal logics with restricted Sahlqvist axioms in terms of the method using metavaluations.

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Citations of this work

Tracking reasons with extensions of relevant logics.Shawn Standefer - 2019 - Logic Journal of the IGPL 27 (4):543-569.
Metavaluations.Ross T. Brady - 2017 - Bulletin of Symbolic Logic 23 (3):296-323.
Some Metacomplete Relevant Modal Logics.Takahiro Seki - 2013 - Studia Logica 101 (5):1115-1141.

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References found in this work

Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
Relevance Logic.Michael Dunn & Greg Restall - 2002 - In D. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic. Kluwer Academic Publishers.
The semantics of entailment — III.Richard Routley & Robert K. Meyer - 1972 - Journal of Philosophical Logic 1 (2):192 - 208.
The semantics of entailment II.Richard Routley & Robert K. Meyer - 1972 - Journal of Philosophical Logic 1 (1):53 - 73.

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