Paraconsistency in Chang's logic with positive and negative truth values

In [1], C. C. Chang introduced a natural generalization of Lukasiewicz infinite valued propositional logic L. In this logic the truth values are extended from the interval [0,1] to the interval [-1,1]. We will call L* the logic whose designated values are those greater or equal than 0. (Chang calls this logic p*[0].) In this semantics, for a truth assignment v the value of the negation is upsilon(-rho) = -nu(rho). This implies that there axe sentences for which nu(rho) = nu(-rho) = 0, that is, both sentences are tautologies. Moreover, the sentence rho --> (-rho-psi) is not a tautology so L* is paraconsistent. Two are the main results of this paper. First we axiomatize the system L-0(*), the logic whose only designated truth value is 0, that is, the paraconsistent sentences of L*. Then, we prove that the categories MV and MV*, whose objects are MV-algebras and MV*-algebras respectively, with their corresponding morphisms, are equivalent. These categories are associated with Lukasiewicz' infinite valued calculus and with Chang's logic L*, respectively.