The Basic Constructive Logic for Absolute Consistency Authors
First Online: 27 August 2008 Received: 08 April 2007 Accepted: 02 July 2008 DOI:
Cite this article as: Méndez, J.M. & Robles, G. J of Log Lang and Inf (2009) 18: 199. doi:10.1007/s10849-008-9077-2 Abstract
In this paper, consistency is understood as absolute consistency (i.e. non-triviality). The basic constructive logic B
Kc6, 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 Kc6 up to contractionless 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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