Relevance logics and intuitionistic negation
José M. Méndez, Gemma Robles · Journal of Applied Non-Classical Logics · 2008
The logic B+ is Routley and Meyer's basic positive logic. We show how to introduce a minimal intuitionistic negation and an intuitionistic negation in B+. The two types of negation are introduced in a wide spectrum of relevance logics built up from B+. It is proved that although all these logics have the characteristic paradoxes of consistency, they lack the K rule (and so, the K axioms).