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→.A→B)→.A→B 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
A. R. Anderson andN. D. Belnap,Entailment: the Logic of Relevance and Necessity, Vol. I, Princeton University Press, Princeton, 1975.
R. K. Meyer,Metacompleteness,Notre Dame Journal of Formal Logic 17 (1976), pp. 501–517.
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The main results of this paper were presented at the ‘Paraconsistent Logic’ conference in Canberra in 1980. The author wishes to thank the participants in that conference for comments and suggestions made at the time.
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Slaney, J.K. A metacompleteness theorem for contraction-free relevant logics. Stud Logica 43, 159–168 (1984). https://doi.org/10.1007/BF00935747
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DOI: https://doi.org/10.1007/BF00935747