Relevance logics, paradoxes of consistency and the K rule II. A non-constructive negation
José M. Méndez, Gemma Robles · Logic and Logical Philosophy · 2007
The logic B+ is Routley and Meyer’s basic positive logic. We define the logics BK+ and BK'+ by adding to B+ the K rule and to BK+ the characteristic S4 axiom, respectively. These logics are endowed with a relatively strong non-constructive negation. We prove that all the logics defined lack the K axiom and the standard paradoxes of consistency.