Relevance logics, paradoxes of consistency and the K rule II. A non-constructive negation
DOI:
https://doi.org/10.12775/LLP.2006.011Keywords
implicative paradoxes, substructural logics, relevance logics, ternary relational semanticsAbstract
The logic B+ is Routley and Meyer’s basic positive logic. We define the logics BK+ and BK'+ by adding to B+ the K rule and to BK+ the characteristic S4 axiom, respectively. These logics are endowed with a relatively strong non-constructive negation. We prove that all the logics defined lack the K axiom and the standard paradoxes of consistency.References
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