American Journal of Systems and Software
ISSN (Print): 2372-708X ISSN (Online): 2372-7071 Website: Editor-in-chief: Josué-Antonio Nescolarde-Selva
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American Journal of Systems and Software. 2014, 2(6), 139-145
DOI: 10.12691/ajss-2-6-1
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Truth Values in t-norm based Systems Many-valued FUZZY Logic

Usó-Doménech J.L.1, Nescolarde-Selva J.1, and Perez-Gonzaga S.1

1Department of Applied Mathematics, University of Alicante, Alicante, Spain

Pub. Date: December 08, 2014

Cite this paper:
Usó-Doménech J.L., Nescolarde-Selva J. and Perez-Gonzaga S.. Truth Values in t-norm based Systems Many-valued FUZZY Logic. American Journal of Systems and Software. 2014; 2(6):139-145. doi: 10.12691/ajss-2-6-1


In t-norm based systems many-valued logic, valuations of propositions form a non-countable set: interval [0,1]. In addition, we are given a set E of truth values p, subject to certain conditions, the valuation v is v=V(p), V reciprocal application of E on [0,1]. The general propositional algebra of t-norm based many-valued logic is then constructed from seven axioms. It contains classical logic (not many-valued) as a special case. It is first applied to the case where E=[0,1] and V is the identity. The result is a t-norm based many-valued logic in which contradiction can have a nonzero degree of truth but cannot be true; for this reason, this logic is called quasi-paraconsistent.

contradiction denier logic coordinations propositions truth value

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