Concept
T-norm fuzzy logics
Overview
T-norm fuzzy logics are a family of non-classical logics, informally delimited by having a semantics that 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 that restrict the t-norm semantics to a subset of the real unit interval (for example, finitely valued Łukasiewicz logics) are usually included in the class as well.
Important examples of t-norm fuzzy logics are monoidal t-norm logic (MTL) of all left-continuous t-norms, basic logic (BL) of all continuous t-norms, product fuzzy logic of the product t-norm, or the nilpotent minimum logic of the nilpotent minimum t-norm. Some independently motivated logics belong among t-norm fuzzy logics, too, for example Łukasiewicz logic (which is the logic of the Łukasiewicz t-norm) or Gödel–Dummett logic (which is the logic of the minimum t-norm).
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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Then the definition of the event-particle associated with the punct is that it is the group of all the {sigma}-primes, where {sigma} has this particular meaning. It is evident that--with this meaning of {sigma}--every abstractive set equal to a {sigma}-prime is itself a {sigma}-prime. Accordingly an event-particle as thus defined is an abstractive element, namely it is the group of those abstractive sets which are…
Alfred North Whitehead, The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919
States what T-norm fuzzy logics is.
Any such select set is called the set of postulates, or premises, from which the reasoning proceeds. The reasoning is nothing else than the exhibition of the whole pattern of general conditions involved in the pattern derived from the selected postulates.
Alfred North Whitehead, Science and the modern world
States what T-norm fuzzy logics is.
All types of series are capable of formal definition, and their properties can be deduced from the principles of symbolic logic by means of the Algebra of Relatives. The notion of a limit, which is fundamental in the greater part of higher mathematics, used to be defined by means of quantity, as a term to which the terms of some series approximate as nearly as we please. But nowadays the limit is defined quite…
Bertrand Russell, Mysticism and Logic and Other Essays
States what T-norm fuzzy logics is.
Philosophers who discussed T-norm fuzzy logics
Related ideas
- First-order logic
- Journal of Symbolic Logic
- Propositional variable
- Truth value
- Kurt Gödel
- Intuitionistic logic
- Logical conjunction
- Propositional logic
- Axiomatic system
- Modus ponens
- Real number
- Three-valued logic
- Rule of inference
- Truth table
- Semantics
- Michael Dummett
- Total order
- Jan Łukasiewicz
- Completeness (logic)
- Logical consequence
- Many-valued logic
- Well-formed formula
- Arity
- Quantifier (logic)
Place in the tradition
Part of First-order logic.