Predicates

Predicates are linguistic and logical expressions that denote properties or relations that can be true or false depending on the objects to which they are applied. In logic, a predicate is a function that takes one or more terms and returns a truth value. A unary predicate P(x) asserts that x has property P; a binary predicate R(x,y) asserts that x bears relation R to y. In first-order logic, formulas consist of predicate symbols, variables, logical connectives, and quantifiers, with the truth of quantified statements depending on an interpretation of the domain.

In linguistics, the predicate is the part of a sentence that asserts something about the subject, typically centered on the verb and its complements. For example, in "The cat sits on the mat," "sits on the mat" is the predicate.

In computer science, a predicate is a function or expression that evaluates to a boolean value. Predicates are used in conditional statements, filters, searches, and automated reasoning. They can be higher-order and may take other predicates as parameters.

Terminology and usage vary by field: predicates may denote properties (unary), relations (binary, ternary, etc.), or more complex conditions. Key ideas include arity, variables, scope, and interpretation. Understanding predicates helps connect abstract logic with grammar, computation, and data querying.