Comparing the Expressive Power of Some Fuzzy Logics Based on Residuated t-norms

In this paper we deal with the expressive power of some logics based on residuated left-continuous t-norms. We investigate the class of truth functions for Nilpotent Minimum, Godel and NMG logics counting the number of different elements and describing normal forms which generalize the classical Boolean sum of minterms and product of maxterms. It turns out that the logics considered in the paper have much greater expressive power than Boolean propositional logic, while the complexity of their normal forms remains almost as manageable as Boolean normal forms.