Extensions of the basic constructive logic for negation-consistency BKC4 defined with a falsity constant

Gemma Robles

Abstract


The logic BKc4 is the basic constructive logic for negation consistency (i.e., absence of any contradiction) in the ternary relational semantics without a set of designated points. In this paper, a number of extensions of BKc4 defined with a propositional falsity constant are defined. It is also proved that negation-consistency is not equivalent to absolute consistency (i.e., non-triviality) in any logic included in positive intermediate logic LC plus the constructive negation of BKc4 and the (constructive) contraposition axioms.

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