Topic summary
Functional predicate
Extracted from the Wikipedia article Function symbol.
Doing without functional predicates
Many treatments of predicate logic don't allow functional predicates, only relational predicates. This is useful, for example, in the context of proving metalogical theorems (such as Gödel's incompleteness theorems), where one doesn't want to allow the introduction of new functional symbols (nor any other new symbols, for that matter). But there is a method of replacing functional symbols with relational symbols wherever the former may occur; furthermore, this is algorithmic and thus suitable for applying most metalogical theorems to the result.