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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 (logic)|model]], a function symbol will be modelled by a [[function (mathematics)|function]].
Specifically, the symbol <i>F</i> in a [[formal language]] is a functional symbol if, [[given any]] symbol <i>X</i> representing an object in the language, <i>F</i>(<i>X</i>) is again a symbol representing an object in that language.
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Then <i>F</i> can be modelled by the set
: [<i>F</i>] := {([<i>X</i>],[<i>F</i>(<i>X</i>)]) : [<i>X</i>] in [<b>T</b>]},
which is simply a [[function (mathematics)|function]] with ___domain [<b>T</b>] and codomain [<b>U</b>].
It is a requirement of a consistent model that [<i>F</i>(<i>X</i>)] = [<i>F</i>(<i>Y</i>)] whenever [<i>X</i>] = [<i>Y</i>].
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