Rules in relevant logic - I: Semantic classification [Book Review]

Journal of Philosophical Logic 23 (2):111 - 137 (1994)
Abstract
We provide five semantic preservation properties which apply to the various rules -- primitive, derived and admissible -- of Hilbert-style axiomatizations of relevant logics. These preservation properties are with respect to the Routley-Meyer semantics, and consist of various truth- preservations and validity-preservations from the premises to the conclusions of these rules. We establish some deduction theorems, some persistence theorems and some soundness and completeness theorems, for these preservation properties. We then apply the above ideas, as best we can, to the classical sentential and predicate calculi, to normal and non- normal modal logics, and to many- valued logics
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References found in this work BETA
Ross T. Brady (1990). The Gentzenization and Decidability of RW. Journal of Philosophical Logic 19 (1):35 - 73.
Max J. Cresswell (1972). The Completeness of $S1$ and Some Related Systems. Notre Dame Journal of Formal Logic 13 (4):485-496.
Kit Fine (1988). Semantics for Quantified Relevance Logic. Journal of Philosophical Logic 17 (1):27 - 59.
Robert K. Meyer & J. Michael Dunn (1969). E, R, and $Gamma$. Journal of Symbolic Logic 34 (3):460-474.
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