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Reports on Mathematical Logic

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No. 42

Gemma ROBLES and Jos\'{e} M. M\'{E}NDEZ

MINIMAL NON-RELEVANT LOGICS WITHOUT THE K AXIOM
A b s t r a c t. The logic B$_{+}$ is Routley and Meyer's basic positive logic. The logic B$_{K+}$ is B$_{+}$
plus the $K$ rule. We add to B$_{K+}$ four intuitionistic-type negations. We show how to extend the resulting logics
within the modal and relevance spectra. We prove that all the logics defined lack the K axiom

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