In propositional logic and in first-order logic, an atomic formula (or simply atom) is either a propositional letter or an n-place predicate letter followed by n variables. An atomic sentence is the same as above except that the n-place predicate letter is followed by n constants or functors.

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; and let p be a propositional letter. Then these are atomic sentences:

• p
• M(a)
• P(b,a,c)

but these atomic formulae are not atomic sentences (because there are free occurrences of variables):

• M(x)
• T(a,z)
• P(x,y,z)

Mathematical logic | 原子句子