In
mathematical logic, monoidal t-norm based logic (or shortly MTL), the logic of left-continuous
t-norm In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in fuzzy logic. A t-norm generalizes intersection (s ...
s, is one of the
t-norm fuzzy logics. It belongs to the broader class of
substructural logics, or logics of
residuated lattices;
[Ono (2003).] it extends the logic of commutative bounded integral residuated lattices (known as Höhle's
monoidal logic, Ono's FL
ew, or
intuitionistic logic without contraction) by the axiom of prelinearity.
Motivation
In
fuzzy logic
Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and complete ...
, rather than regarding statements as being either true or false, we associate each statement with a numerical ''confidence'' in that statement. By convention the confidences range over the unit interval