Extending the Monoidal T-norm Based Logic with an Independent Involutive Negation

In this paper we investigate the logic MTL obtained by extending Esteva and Godo’s logic MTL with an involutive negation not dependent on the t-norm and with the Baaz’s operator . Moreover, we also introduce and study the related predicate calculus MTL8 . Algebraic and standard completeness results are shown to hold for both MTL and MTL8 .