atomic-formula
See also
Definition
An atomic-formula is a formula that is not composed of a connective and terms. Equivalently, it is a leaf is a formula tree.
Note that several definitions may be found in the litterature. [Coo09, p. 20] defines it as a single-n-ary predicate followed by n singular terms. In the context of punctilious, we rather adopt the definition proposed by [MS13, p. 55] where variables, true, and false are examples of atomic formula and where single-predicate formulae are considered compound formulae.
Quotes
An atomic formula (or atom, or simple formula) is a formula that consists of a single n-ary predicate followed by n singular terms. Note that the terms might be simple or complex, and might be, or contain, either constants or variables. [Coo09, p. 20]
atomic formula Let L be a first order language. An atomic formula is an expression which has the form P(t1,…,tn), where P is an n-place predicate symbol of L and t1,…,tn are terms of L. If L contains equality (=), then = is viewed as a two-place predicate. Consequently, if t1 and t2 are terms, then t1 = t2 is an atomic formula. [CH01, p. 5]
(…) A statement written in propositional logic is called a propositional formula, and is either:
an atomic formula, typically represented by a variable such as P, Q, or R; or
a compound formula, in which case it is built up using the above propositional connectives as summarised in Figure 1.1
There are two special atomic propositional formulae, true (representing the proposition which is always true) and false (representing the proposition which is always false).
The above define the syntax of the language of propositional formulae. (…) [MS13, p. 55]
Sources
[Coo09]