A metacompleteness theorem for contraction-free relevant logics
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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.
KeywordsResearch Programme Close Relative Mathematical Logic Analogous Result Computational Linguistic
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