The basic constructive logic for negation-consistency

Abstract
In this paper, consistency is understood in the standard way, i.e. as the absence of a contradiction. The basic constructive logic BKc4, which is adequate to this sense of consistency in the ternary relational semantics without a set of designated points, is defined. Then, it is shown how to define a series of logics by extending BKc4 up to minimal intuitionistic logic. All logics defined in this paper are paraconsistent logics.
Keywords Constructive negation  Substructural logics  Ternary relational semantics  Paraconsistent logic
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