A Variety of DeMorgan Negations in Relevant Logics

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