Function symbol: Difference between revisions

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Revision as of 22:17, 30 September 2009

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In a [[model (logic)|model]], a function symbol will be modelled by a [[function (mathematics)|function]].

Specifically, the symbol ''F'' in a [[Formal language (logic)|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 [[0 (number)|zero]] variables is simply a [[constant]] symbol.