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- Functional_predicate abstract "In formal logic and related branches of mathematics, a functional predicate, or function symbol, is a logical symbol that may be applied to an object term to produce another object term.Functional predicates are also sometimes called mappings, but that term has other meanings as well.In a model, a function symbol will be modelled by a function.Specifically, the symbol F in a formal language is a functional symbol if, given any symbol X representing an object in the language, F(X) is again a symbol representing an object in that language.In typed logic, F is a functional symbol with domain type T and codomain type U if, given any symbol X representing an object of type T, F(X) is a symbol representing an object of type U.One can similarly define function symbols of more than one variable, analogous to functions of more than one variable; a function symbol in zero variables is simply a constant symbol.Now consider a model of the formal language, with the types T and U modelled by sets [T] and [U] and each symbol X of type T modelled by an element [X] in [T].Then F can be modelled by the setwhich is simply a function with domain [T] and codomain [U].It is a requirement of a consistent model that [F(X)] = [F(Y)] whenever [X] = [Y].".
- Functional_predicate wikiPageID "174908".
- Functional_predicate wikiPageRevisionID "543597668".
- Functional_predicate hasPhotoCollection Functional_predicate.
- Functional_predicate subject Category:Model_theory.
- Functional_predicate comment "In formal logic and related branches of mathematics, a functional predicate, or function symbol, is a logical symbol that may be applied to an object term to produce another object term.Functional predicates are also sometimes called mappings, but that term has other meanings as well.In a model, a function symbol will be modelled by a function.Specifically, the symbol F in a formal language is a functional symbol if, given any symbol X representing an object in the language, F(X) is again a symbol representing an object in that language.In typed logic, F is a functional symbol with domain type T and codomain type U if, given any symbol X representing an object of type T, F(X) is a symbol representing an object of type U.One can similarly define function symbols of more than one variable, analogous to functions of more than one variable; a function symbol in zero variables is simply a constant symbol.Now consider a model of the formal language, with the types T and U modelled by sets [T] and [U] and each symbol X of type T modelled by an element [X] in [T].Then F can be modelled by the setwhich is simply a function with domain [T] and codomain [U].It is a requirement of a consistent model that [F(X)] = [F(Y)] whenever [X] = [Y].".
- Functional_predicate label "Functional predicate".
- Functional_predicate label "Symbol funkcyjny".
- Functional_predicate label "泛函谓词".
- Functional_predicate sameAs Symbol_funkcyjny.
- Functional_predicate sameAs m.017ml9.
- Functional_predicate sameAs Q5508846.
- Functional_predicate sameAs Q5508846.
- Functional_predicate wasDerivedFrom Functional_predicate?oldid=543597668.
- Functional_predicate isPrimaryTopicOf Functional_predicate.