A Variety of DeMorgan Negations in Relevant Logics

Abstract

The present paper is inspired by Sylvan and Plumwood’s logic
BM defined in “Non-normal relevant logics” and by their treatment
of negation with the ∗-operator in “The semantics of first-degree en-
tailment”. Given a positive logic L including Routley and Meyer’s
basic positive logic and included in either the positive fragment of E
or in that of RW, we investigate the essential De Morgan negation ex-
pansions of L and determine all the deductive relations they maintain
to each other. A Routley-Meyer semantics is provided for each logic
defined in the paper.