Admissible Rules and the Leibniz Hierarchy

Notre Dame Journal of Formal Logic 57 (4):569-606 (2016)
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Abstract

This paper provides a semantic analysis of admissible rules and associated completeness conditions for arbitrary deductive systems, using the framework of abstract algebraic logic. Algebraizability is not assumed, so the meaning and significance of the principal notions vary with the level of the Leibniz hierarchy at which they are presented. As a case study of the resulting theory, the nonalgebraizable fragments of relevance logic are considered.

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10.1215/00294527-3671151

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Citations of this work

Almost structural completeness; an algebraic approach.Wojciech Dzik & Michał M. Stronkowski - 2016 - Annals of Pure and Applied Logic 167 (7):525-556.
Order algebraizable logics.James G. Raftery - 2013 - Annals of Pure and Applied Logic 164 (3):251-283.
Hereditarily structurally complete positive logics.Alex Citkin - 2020 - Review of Symbolic Logic 13 (3):483-502.

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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.
A survey of abstract algebraic logic.J. M. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):13 - 97.
Protoalgebraic logics.W. J. Blok & Don Pigozzi - 1986 - Studia Logica 45 (4):337 - 369.
Equivalence of Consequence Operations.W. J. Blok & Bjarni Jónsson - 2006 - Studia Logica 83 (1-3):91-110.

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