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:
“No atomic physicist has to worry, people will always want to kill other people on a mass scale. Sure, he’s got the fridge full of sausages and spring water.”
—William Burroughs (b. 1914)
“Parents’ accepting attitudes can help children learn to be open and tolerant. Parents can explain unfamiliar behavior or physical handicaps and show children that the appropriate response to differences should be interest rather than revulsion.”
—Dian G. Smith (20th century)
“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)