Minimal Non-relevant Logics Without The K Axiom

Gemma Robles
Universidad de León
José M. Méndez
Universidad de Salamanca
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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