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:
“Other centuries had their driving forces. What will ours have been when men look far back to it one day? Maybe it won’t be the American Century, after all. Or the Russian Century or the Atomic Century. Wouldn’t it be wonderful, Phil, if it turned out to be everybody’s century, when people all over the world—free people—found a way to live together? I’d like to be around to see some of that, even the beginning.”
—Moss Hart (1904–1961)
“As to what we call the masses, and common men;Mthere are no common men. All men are at last of a size; and true art is only possible, on the conviction that every talent has its apotheosis somewhere. Fair play, and an open field, and freshest laurels to all who have won them!”
—Ralph Waldo Emerson (1803–1882)
“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)