t-norm

This is well-defined only if the t-norm is left-continuous.

Fuzzy Logic Hajek, Petr 2006

This has excellent properties thanks to the fact that Łukasiewicz t-norm is the only continuous t-norm whose residuum is continuous.

Fuzzy Logic Hajek, Petr 2006

Gottwald & Hajek 2005 and on t-norm based predicate logics

Fuzzy Logic Hajek, Petr 2006

Cintula 2006 and two recent survey papers: on t-norm based propositional logics

Fuzzy Logic Hajek, Petr 2006

Esteva, F. and Godo, L. (2001): Monoidal t-norm based logic: towards a logic for left-continuous t-norms, Fuzzy Sets Systems 124, 271-288.

Many-Valued Logic Gottwald, Siegfried 2004

Actually one is able to axiomatize t-norm based systems for some particular classes of t-norms.

Many-Valued Logic Gottwald, Siegfried 2004

G ˆž, and also the product logic which has the usual arithmetic product as its basic t-norm.

Many-Valued Logic Gottwald, Siegfried 2004

Sufficiently well understood is only the further subclass of continuous t-norms: they are nicely composed out of isomorphic copies of the Łukasiewicz t-norm, the product t-norm, and the Gödel t-norm, i.e. the min-operation, as explained e.g. in Gottwald (2001).

Many-Valued Logic Gottwald, Siegfried 2004

The axiomatization of further t-norm based systems, as well as the question for t-norm based quantifiers, are recent research problems.

Many-Valued Logic Gottwald, Siegfried 2004

This implication connective is connected with the t-norm T by the crucial adjointness condition

Many-Valued Logic Gottwald, Siegfried 2004