The Basic Constructive Logic for Absolute Consistency
- First Online:
In this paper, consistency is understood as absolute consistency (i.e. non-triviality). The basic constructive logic BKc6, 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 BKc6 up to contractionless intuitionistic logic. All logics defined in this paper are paraconsistent logics.
KeywordsConstructive negation Substructural logics Ternary relational semantics Paraconsistent logic
Unable to display preview. Download preview PDF.
- Robles, G., & Méndez, J. M. (2008a). On defining constructive negation in logics of entailment. In J. L. Béziau (Ed.), Papers in logics UNILOG 2005 (forthcoming).Google Scholar
- Robles, G., & Méndez, J. M. (in preparation). Strong paraconsistency and the basic constructive logic for an even weaker sense of consistency.Google Scholar
- Robles, G. and Méndez (2008b) Relevance logics, paradoxes of consistency and the K rule. Logique et Analyse 198: 129–145 (An abstract of this paper was read at the Logic Colloquium 2006, Nijmegen, Holland, 27 July–2 August 2006)Google Scholar
- Routley R. et al (1982) Relevant logics and their rivals (Vol. 1). Atascadero, CA, Ridgeview Publishing CoGoogle Scholar
- Slaney, J. (1995). MaGIC, matrix generator for implication connectives: Version 2.1, notes and guide. Canberra: Australian National University, URL: http://users.rsise.anu.edu.au/~jks