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)
“I open with a clock striking, to beget an awful attention in the audience—it also marks the time, which is four o’clock in the morning, and saves a description of the rising sun, and a great deal about gilding the eastern hemisphere.”
—Richard Brinsley Sheridan (1751–1816)
“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)