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:
but these are not atomic sentences:
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.
