Extensions of the basic constructive logic for weak consistency BKc1 defined with a falsity constant

Gemma Robles

DOI: http://dx.doi.org/10.12775/LLP.2007.010

Abstract


The logic BKc1 is the basic constructive logic for weak consistency (i.e., absence of the negation of a theorem) in the ternary relational semantics without a set of designated points. In this paper, a number of extensions of B Kc1 defined with a propositional falsity constant are defined. It is also proved that weak consistency is not equivalent to negation-consistency or absolute consistency (i.e., non-triviality) in any logic included in positive contractionless intermediate logic LC plus the constructive negation of BKc1 and the (constructive) contraposition axioms.

Keywords


weak consistency; constructive falsity; ternary relational semantics; substructural logics, paraconsistent logics

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References


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