A metacompleteness theorem for contraction-free relevant logics

Studia Logica 43 (1-2):159 - 168 (1984)
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Abstract

I note that the logics of the relevant group most closely tied to the research programme in paraconsistency are those without the contraction postulate(A.AB).AB and its close relatives. As a move towards gaining control of the contraction-free systems I show that they are prime (that wheneverA B is a theorem so is eitherA orB). The proof is an extension of the metavaluational techniques standardly used for analogous results about intuitionist logic or the relevant positive logics.

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References found in this work

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.
Metacompleteness.Robert K. Meyer - 1976 - Notre Dame Journal of Formal Logic 17 (4):501-516.
Negation disarmed.Robert K. Meyer - 1976 - Notre Dame Journal of Formal Logic 17 (2):184-190.

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