High Quality Content by WIKIPEDIA articles! T-norm fuzzy logics are a family of non-classical logics, informally delimited by having a semantics which takes the real unit interval [0, 1] for the system of truth values and functions called t-norms for permissible interpretations of conjunction. They are mainly used in applied fuzzy logic and fuzzy set theory as a theoretical basis for approximate reasoning. T-norm fuzzy logics belong in broader classes of fuzzy logics and many-valued logics. In order to generate a well-behaved implication, the t-norms are usually required to be left-continuous; logics of left-continuous t-norms further belong in the class of substructural logics, among which they are marked with the validity of the law of prelinearity, (A ? B) ? (B ? A). Both propositional and first-order (or higher-order) t-norm fuzzy logics, as well as their expansions by modal and other operators, are studied. Logics which restrict the t-norm semantics to a subset of the real unit interval (for example, finitely valued ?ukasiewicz logics) are usually included in the class as well.

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