The Basic Constructive Logic for Negation-Consistency
First Online: 27 November 2007 Received: 31 March 2007 Accepted: 09 November 2007 DOI:
10.1007/s10849-007-9056-z Cite this article as: Robles, G. J of Log Lang and Inf (2008) 17: 161. doi:10.1007/s10849-007-9056-z Abstract
In this paper, consistency is understood in the standard way, i.e. as the absence of a contradiction. The basic constructive logic B
Kc4, 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 B Kc4 up to minimal intuitionistic logic. All logics defined in this paper are paraconsistent logics. Keywords Constructive negation Substructural logics Ternary relational semantics Paraconsistent logic References
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