Abstract
A prepositional logic S has the “Converse Ackermann Property” (CAP) if (A→B)→C is unprovable in S when C does not contain →. In “A Routley-Meyer semantics for Converse Ackermann Property” (Journal of Philosophical Logic, 16 (1987), pp. 65–76) I showed how to derive positive logical systems with the CAP. There I conjectured that each of these positive systems were compatible with a so-called “semiclassical” negation. In the present paper I prove that this conjecture was right. Relational Routley-Meyer type semantics are provided for each one of the resulting systems (the positive systems plus the semiclassical negation).
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References
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Méndez, J.M. Converse Ackermann Croperty and semiclassical negation. Stud Logica 47, 159–168 (1988). https://doi.org/10.1007/BF00370290
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DOI: https://doi.org/10.1007/BF00370290