Classically complete modal relevant logics

Mathematical Logic Quarterly 39 (1):165-177 (1993)
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Abstract

A variety of modal logics based on the relevant logic R are presented. Models are given for each of these logics and completeness is shown. It is also shown that each of these logics admits Ackermann's rule γ and as a corollary of this it is proved that each logic is a conservative extension of its counterpart based on classical logic, hence we call them “classically complete”. MSC: 03B45, 03B46

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Edwin Mares
Victoria University of Wellington

References found in this work

Semantical Considerations on Modal Logic.Saul Kripke - 1963 - Acta Philosophica Fennica 16:83-94.
Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
Entailment: The Logic of Relevance and Neccessity, Vol. I.Alan Ross Anderson & Nuel D. Belnap - 1975 - Princeton, N.J.: Princeton University Press. Edited by Nuel D. Belnap & J. Michael Dunn.
Entailment: The Logic of Relevance and Necessity.[author unknown] - 1975 - Studia Logica 54 (2):261-266.
Models for entailment.Kit Fine - 1974 - Journal of Philosophical Logic 3 (4):347 - 372.

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