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First-order predicate

Logical statement with variables, predicates, and quantifiers over objects

Wikipedia contributorsAdapted for Fathomly · View authors
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Source updated March 26, 2026

In mathematical logic, a first-order predicate is a predicate that takes only individual(s) constants or variables as argument(s). Compare second-order predicate and higher-order predicate.

This is not to be confused with a one-place predicate or monad, which is a predicate that takes only one argument. For example, the expression "is a planet" is a one-place predicate, while the expression "is father of" is a two-place predicate.

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This article is adapted from the Wikipedia article “First-order predicate”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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Related topics

First-order logic

In mathematics, philosophy, linguistics, and computer science, first-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a type of formal system. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables.

Monadic predicate calculus

In logic, the monadic predicate calculus is the fragment of first-order logic (also called predicate calculus) in which all relation symbols in the signature are monadic (that is, they take only one argument), and there are no function symbols. In other words, all atomic formulas are of the form P ( t ) {\displaystyle P(t)} , where P {\displaystyle P} is a relation symbol and t {\displaystyle t} is a term.