Atomic sentence - Definition and Overview

In propositional calculus and in predicate calculus, an atomic sentence is an atomic formula which contains no variables. Otherwise the atomic formula is an open sentence.

As examples, let P, M, T be predicate letters; let a, b, c, etc. be constant terms; but let x, y, z be variable terms. Then these are atomic sentences:

• P
• M(a)
• T(b, c)
• P₂(b,a,c)

but these are not atomic sentences:

• M(x)
• T(a,z)
• P₂(x,y,z)

In prop.calc. all atomic formulas are atomic sentences, because atomic propositions correspond to 0-ary predicates, but a predicate must be at least unary in order to be able to introduce variable terms.