Science and Education Publishing American Journal of Systems and Software 2 6 2014 12 08 Truth Values in t-norm based Systems Many-valued FUZZY Logic 139 145 EN Usó-Doménech J.L. Nescolarde-Selva J. Department of Applied Mathematics, University of Alicante, Alicante, Spain Perez-Gonzaga S. AJSS2014261 10.12691/ajss-2-6-1 2014 11 28 2014 12 04 2014 12 08 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.