Consider the following expressions in first order logic over a signature containing the constant symbols and for the numbers 0 and 1, respectively, a unary function symbol for the successor function and a binary function symbol for addition.
are ground terms;
are ground terms;
are ground terms;
and are terms, but not ground terms;
and are ground formulae.
Formal definitions
What follows is a formal definition for first-order languages. Let a first-order language be given, with the set of constant symbols, the set of functional operators, and the set of predicate symbols.
Ground term
A ground term is a term that contains no variables. Ground terms may be defined by logical recursion (formula-recursion):
Elements of are ground terms;
If is an -ary function symbol and are ground terms, then is a ground term.
Every ground term can be given by a finite application of the above two rules (there are no other ground terms; in particular, predicates cannot be ground terms).
Roughly speaking, the Herbrand universe is the set of all ground terms.
Ground atom
A ground predicate, ground atom or ground literal is an atomic formula all of whose argument terms are ground terms.
If is an -ary predicate symbol and are ground terms, then is a ground predicate or ground atom.
Dalal, M. (2000), "Logic-based computer programming paradigms", in Rosen, K.H.; Michaels, J.G. (eds.), Handbook of discrete and combinatorial mathematics, p. 68