  The axiomatization of further t-norm based systems, as well as the question for t-norm based quantifiers, are recent research problems. The main focus is given by the following two aspects which concern modifications of the expressive power of these t-norm based systems: (i) strengthenings of this expressibility by forming systems with additional negation operators or with multiple t-norm based conjunction operations; (ii) modifications of this expressibility e.g. by deleting the truth degree constant \(\uO\) from the language, but adding an implication connective to the basic vocabulary, and (iii) generalizations which modify the basic t-norms into non-commutative “pseudo-t-norms” and thus lead to logics with non-commutative conjunction connectives. Surveys for those developments had been given by Gottwald/Hájek (2005), Gottwald (2008), and Cintula/Hájek (2010). 