Affiliation:
1. Department of Philosophy, University of Bergen PB 7805, 5020 Bergen, Norway
Abstract
Abstract
Many relevant logics can be conservatively extended by Boolean negation. Mares showed, however, that E is a notable exception. Mares’ proof is by and large a rather involved model-theoretic one. This paper presents a much easier proof-theoretic proof which not only covers E but also generalizes so as to also cover relevant logics with a primitive modal operator added. It is shown that from even very weak relevant logics augmented by a weak K-ish modal operator, and up to the strong relevant logic R with a S5 modal operator, all fail to be conservatively extended by Boolean negation. The proof, therefore, also covers Meyer and Mares’ proof that NR—R with a primitive S4-modality added—also fails to be conservatively extended by Boolean negation.
Publisher
Oxford University Press (OUP)
Reference23 articles.
1. Begründung einer strengen Implikation;Ackermann,1956
2. Modalities in Ackermann’s “rigorous implication”;Anderson;Journal of Symbolic Logic,1959
3. Entailment and relevance;Belnap;Journal of Symbolic Logic,1960
4. Gentzenizations of relevant logics with distribution;Brady;Journal of Symbolic Logic,1996
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