About: T-norm fuzzy logics

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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.

Attributes	Values
rdfs:label	Lógicas difusas de T-norma (pt) T-norm fuzzy logics (en)
rdfs:comment	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. (en) Lógicas difusas de T-norma são uma família de lógicas não clássicas, informalmente delimitada por ter uma semântica que toma o intervalo da unidade real de [0, 1] para o sistema de valores verdade e de funções chamadas de para possíveis interpretações de conjunção lógica. Elas são usadas principalmente em lógica difusa aplicada e teorias de conjuntos difusos como uma base teórica para o raciocínio aproximado. (pt)
dcterms:subject	Fuzzy logic
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Wikipage revision ID	1088972822 (xsd:integer)
Link from a Wikipage to another Wikipage	Product fuzzy logic Propositional formula Algebraic semantics (mathematical logic) Algebraic structure Join (mathematics) Unary operation Deduction theorem Intermediate logic Intuitionistic logic Meet (mathematics) Modal operator Arity Logical conjunction Logical implication Completeness (logic) Computational complexity Propositional logic Many-valued logic Fuzzy logic Total order Truth table Truth value Fuzzy logic Fuzzy set Countable Lattice (order) T-norm Three-valued logic First-order logic Well-formed formula Quantifier (logic) Gödel Atomic formula Involution (mathematics) Jan Łukasiewicz Tautology (logic) Łukasiewicz logic Higher-order logic Modus ponens BL (logic) Idempotence Michael Dummett Real number Petr Hájek Monoidal t-norm logic Semantics Propositional variable Residuated lattice Non-classical logic Substructural logic Left-continuous Soundness theorem Basic fuzzy logic Nullary Truth-functional dbr:Nilpotent_minimum_logic dbr:ŁΠ
sameAs	T-norm fuzzy logics T-norm fuzzy logics T-norm fuzzy logics T-norm fuzzy logics
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has abstract	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 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). (en) Lógicas difusas de T-norma são uma família de lógicas não clássicas, informalmente delimitada por ter uma semântica que toma o intervalo da unidade real de [0, 1] para o sistema de valores verdade e de funções chamadas de para possíveis interpretações de conjunção lógica. Elas são usadas principalmente em lógica difusa aplicada e teorias de conjuntos difusos como uma base teórica para o raciocínio aproximado. As famílias de lógica difusa de t-norma fazem parte de classes mais amplas de lógica difusa e de lógica multivalorada. A fim de gerar uma implicação bem comportada, as t-normas geralmente são necessárias que sejam funções contínuas; lógicas de t-norma de função continua pertencem à classe de lógica subestrutural, entre os quais estão assinalados com a validade da lei da pré-linearidade, (A → B) ∨ (B → A). Tanto as lógicas difusas de t-norma proposicional e de primeira ordem (ou de ordem superior), bem como suas expansões por operador modal e outros operadores, são estudados. Lógicas que restringem a semântica de t-norma a um subconjunto do intervalo de unidade real (por exemplo, Lógicas de Łukasiewicz finitamente valorizadas) são normalmente incluídos na classe. Exemplos importantes de lógicas difusas de t-norma são as lógicas monoidais de t-norma (MTL) de todas t-normas de função contínua à esquerda, de todas t-normas contínuas, produto de lógica difusa do produto de t-normas, ou o nilpotent mínimum logic da t-norma nilpotent mínima. Algunas lógicas motivadas independentemente pertencem à lógica difusa de t-norma também, como por exemplo a lógica de Łukasiewicz (que é a lógica da t-norma Łukasiewicz) ou a lógica de Gödel–Dummett (que é a lógica da t-norma mínima). (pt)
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is Link from a Wikipage to another Wikipage of	Infinite-valued logic Construction of t-norms Adaptive neuro fuzzy inference system Admissible rule Fuzzy logic T-norm First-order logic Delta Involution (mathematics) Hypercomputation Łukasiewicz logic BL (logic) Monoidal t-norm logic Finite-valued logic T-norm based fuzzy logic T-norm based fuzzy logics T-norm fuzzy logic T-norm logic T-norm logics
is Wikipage redirect of	T-norm based fuzzy logic T-norm based fuzzy logics T-norm fuzzy logic T-norm logic T-norm logics
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