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

Authors:
Takahiro Seki
Affiliations:
University Evaluation Center, Headquarters for Strategy and Planning, Niigata University, Niigata City, Japan 950-2181
Venue:
Studia Logica
Year:
2012

Citing 4
Cited 1

Modal logic

Modal logic
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151

Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
The γ-admissibility of Relevant Modal Logics I -- The Method of Normal Models

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

Studia Logica

Some Metacomplete Relevant Modal Logics

Studia Logica

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Abstract

The admissibility of Ackermann's rule 驴 is one of the most important problems in relevant logics. The admissibility of 驴 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 驴 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 驴 in relevant modal logics based on modern algebraic models.