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Definition: Predicate of a Logical Calculus

Let $L$ be a logical calculus, $U$ the domain of discourse, and $I(U,L)$ the corresponding interpretation with the valuation function $[[]]_I$.

A predicate is a non-empty string over an alphabet $s\in L$ interpreted as a relation \(R\subseteq U^n\) taking \(n\) input arguments from the domain of discourse.

The natural number \(n\ge 1\) of arguments of the predicate is (as for functions) called its arity. Special cases of arities are:

• \(n=1\): Unary predicates
• \(n=2\): Binary predicates
• \(n=3\): Ternary predicates
• generally \(n\)-nary predicates

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References

Bibliography

1. Hoffmann, Dirk W.: "Grenzen der Mathematik - Eine Reise durch die Kerngebiete der mathematischen Logik", Spektrum Akademischer Verlag, 2011