An Algebraic Proof of the Admissibility of γ in Relevant Modal Logics

Studia Logica 100 (6):1149-1174 (2012)
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The admissibility of Ackermann's rule γ is one of the most important problems in relevant logics. The admissibility of γ was first proved by an algebraic method. However, the development of Routley-Meyer semantics and metavaluational techniques makes it possible to prove the admissibility of γ using the method of normal models or the method using metavaluations, and the use of such methods is preferred. This paper discusses an algebraic proof of the admissibility of γ in relevant modal logics based on modern algebraic models



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Neighbourhood Semantics for Modal Relevant Logics.Nicholas Ferenz & Andrew Tedder - 2023 - Journal of Philosophical Logic 52 (1):145-181.
Some Metacomplete Relevant Modal Logics.Takahiro Seki - 2013 - Studia Logica 101 (5):1115-1141.

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References found in this work

Relevance Logic.Michael Dunn & Greg Restall - 1983 - In Dov M. Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic. Dordrecht, Netherland: Kluwer Academic Publishers.
The semantics of entailment — III.Richard Routley & Robert K. Meyer - 1972 - Journal of Philosophical Logic 1 (2):192 - 208.
Reduced models for relevant logics without ${\rm WI}$.John K. Slaney - 1987 - Notre Dame Journal of Formal Logic 28 (3):395-407.

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