Predicate

A predicate is an expression that represents a property of objects or a relation among them. In logic, applying it to suitable arguments yields a proposition that can be true or false.

Proposition: A declarative content that is true or false. Applying a predicate to arguments produces a proposition with a truth value.
First-order logic: A formal system for reasoning about objects, properties, and relations using quantifiers and variables. It supplies the standard formal language in which predicates are interpreted.
Function (mathematics): A mapping that assigns each input in its domain exactly one output. Functions return objects, while predicates classify argument tuples as satisfying or not.
Predicate logic: A logical system that represents objects, their properties, and relations using predicates and quantifiers. It uses predicates to express structured claims beyond whole-proposition logic.
Variable (mathematics): A symbol that can stand for an element of a specified domain. Variables occupy argument positions in predicates before objects are assigned.
Quantifier: An operator that specifies how many objects in a domain satisfy a condition. Quantifiers bind variables in predicate expressions, as in 'every object has a property.'
Propositional variable: A symbol in propositional logic that stands for a complete proposition. Unlike a predicate, it has no open argument positions for objects.
Relational database: A database organized as tables of rows and columns representing relations. Query conditions act like predicates that select rows satisfying specified properties.
Domain of discourse: The set of objects over which variables and quantifiers range. A domain determines which objects a predicate can apply to.
Interpretation (logic): An assignment of meanings to the nonlogical symbols of a formal language within a domain. An interpretation assigns predicates extensions that determine which arguments satisfy them.

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