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)
“Some collaboration has to take place in the mind between the woman and the man before the art of creation can be accomplished. Some marriage of opposites has to be consummated. The whole of the mind must lie wide open if we are to get the sense that the writer is communicating his experience with perfect fullness.”
—Virginia Woolf (1882–1941)
“That’s the great danger of sectarian opinions, they always accept the formulas of past events as useful for the measurement of future events and they never are, if you have high standards of accuracy.”
—John Dos Passos (1896–1970)