Atomic and Open Formulas
An atomic formula is a formula that contains no logical connectives nor quantifiers, or equivalently a formula that has no strict subformulas. The precise form of atomic formulas depends on the formal system under consideration; for propositional logic, for example, the atomic formulas are the propositional variables. For predicate logic, the atoms are predicate symbols together with their arguments, each argument being a term.
According to some terminology, an open formula is formed by combining atomic formulas using only logical connectives, to the exclusion of quantifiers. This has not to be confused with a formula which is not closed.
Read more about this topic: Well-formed Formula
Famous quotes containing the words atomic, open and/or formulas:
“Take adultery or theft.
Merely sins.
It is evil who dines on the soul,
stretching out its long bone tongue.
It is evil who tweezers my heart,
picking out its atomic worms.”
—Anne Sexton (1928–1974)
“Thoroughly to unfold the labyrinths of the human mind is an arduous task.... In order to dive into those recesses and lay them open to the reader in a striking and intelligible manner, ‘tis necessary to assume a certain freedom in writing, not strictly perhaps within the limits prescribed by rules.”
—Sarah Fielding (1710–1768)
“It is sentimentalism to assume that the teaching of life can always be fitted to the child’s interests, just as it is empty formalism to force the child to parrot the formulas of adult society. Interests can be created and stimulated.”
—Jerome S. Bruner (20th century)