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:
“The atomic bomb certainly is the most powerful of all weapons, but it is conclusively powerful and effective only in the hands of the nation which controls the sky.”
—Lyndon Baines Johnson (1908–1973)
“The attempt to be an ideal parent, that is, to behave correctly toward the child, to raise her correctly, not to give to little or too much, is in essence an attempt to be the ideal child—well behaved and dutiful—of one’s own parents. But as a result of these efforts the needs of the child go unnoticed. I cannot listen to my child with empathy if I am inwardly preoccupied with being a good mother; I cannot be open to what she is telling me.”
—Alice Miller (20th century)
“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)