A Variety of DeMorgan Negations in Relevant Logics

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Australasian Journal of Logic 20 (2):348-374 (2023)
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Abstract

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.

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10.26686/ajl.v20i2.8311

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Author Profiles

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

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