The Basic Constructive Logic for Negation-Consistency
- 50 Downloads
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.
KeywordsConstructive negation Substructural logics Ternary relational semantics Paraconsistent logic
Unable to display preview. Download preview PDF.
- Méndez J.M. (1987). Axiomatizing E→ and R→ with Anderson and Belnap’s ‘strong and natural’ list of valid entailments. Bulletin of the Section of Logic 16, 2–10Google Scholar
- Priest, G., & Tanaka, K. (2004). Paraconsistent Logic. In E. N. Zalta (Ed.), The Standford Encyclopedia of Philosophy. Winter 2004 Edition. URL: http://plato.stanford.edu/archives/win2004/entries/logic-paraconsistent/.
- Robles G., Méndez J.M. (2004). The logic B and the reductio axioms. Bulletin of the Section of Logic 33(2): 87–94Google Scholar
- Robles, G., & Méndez, J. M. (2007). The basic constructive logic for a weak sense of consistency. Journal of Logic Language and Information. DOI 10.1007/s10849-007-9042-5.
- Robles, G., & Méndez, J. M. (In preparation). The basic constructive logic for an even weaker sense of consistency.Google Scholar
- Robles G., Méndez J.M., Salto F. (2005). Minimal negation in the ternary relational semantics. Reports on Mathematical Logic 39, 47–65Google Scholar
- Robles, G., Méndez, J. M., & Salto, F. (2007). Relevance logics, paradoxes of consistency and the K rule, Logique et Analyse, 198, 129–145. (An abstract of this paper presented 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 Co.Google Scholar
- Slaney, J. (1995). MaGIC, Matrix Generator for Implication Connectives: Version 2.1, Notes and Guide. Canberra: Australian National University.Google Scholar