Predikaatset

Predikaatset (often called the predicate set or signature in English) refers to the collection of predicate symbols used in a formal language, together with their arities. In first-order logic, a predikaatset includes all unary, binary, and higher-arity predicate symbols that appear in the language.

Each predicate symbol P has an arity n, and does not by itself denote a concrete relation until an interpretation assigns to P a subset P^I of D^n, where D is the domain of discourse. The predikaatset thus determines the potential building blocks for atomic formulas such as P(x1,...,xn).

A language's vocabulary (predikaatset) is extended by adding new predicate symbols, increasing its expressive power. Atomic formulas formed from these symbols, variables, and terms serve as the basis for more complex formulas using logical connectives and quantifiers.

Examples: unary predicates isEven(x), isRed(x); binary predicates likes(x,y), greaterThan(x,y). In a given interpretation, isEven^I might be the set of even numbers in D.

In model theory, a structure M with domain D and interpretation I assigns to each predicate symbol its relation. The truth of a sentence is evaluated relative to M.

Terminology: the term "predikaatset" corresponds to "signature" or "vocabulary" in English-language texts. It is a foundational concept for specifying what relations the language can express.