Atomic formula

An atomic formula is a logical formula with no connectives or quantifiers, typically a predicate applied to terms or an equality between terms.

First-order term: A variable or expression denoting an object in first-order logic. Terms supply the arguments of predicates and the sides of equalities.
Interpretation (logic): An assignment of meanings to the nonlogical symbols of a formal language. An interpretation assigns predicates relations and terms denotations, determining whether an atom is true.
First-order logic: A formal logic whose quantifiers range over individual objects. Atomic formulas are the quantifier-free base cases in first-order formula construction.
Molecular formula (logic): A formula formed by combining simpler formulas with logical connectives. A molecular formula contains connective structure absent from an atom.
Predicate symbol: A symbol that expresses a relation or property when applied to terms. Applying a predicate symbol to the right number of terms forms an atomic formula.
Satisfaction (logic): A relation specifying when a structure and assignment make a formula true. Satisfaction states precisely when an atomic formula holds under an assignment.
Predicate logic: A formal logic that represents properties and relations using predicates and quantifiers. Its statements are built from predicate applications, equality, and logical operators.
Literal (mathematical logic): An atomic formula or its negation. A literal may be negated, whereas an atomic formula itself has no connective.
Equality (logic): A logical relation expressing that two terms denote the same object. Equality between terms is atomic even without a predicate symbol.
Structure (mathematical logic): A domain together with interpretations of the symbols in a formal language. The structure supplies the objects and relations evaluated by atomic formulas.

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Existential quantificationRelated: An existential quantifier can bind a variable in an atomic formula.