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:
“When man entered the atomic age, he opened a door into a new world. What we eventually find in that new world, nobody can predict.”
—Ted Sherdeman. Gordon Douglas. Dr. Medford (Edmund Gwenn)
“I have passed down the river before sunrise on a summer morning, between fields of lilies still shut in sleep; and when, at length, the flakes of sunlight from over the bank fell on the surface of the water, whole fields of white blossoms seemed to flash open before me, as I floated along, like the unfolding of a banner, so sensible is this flower to the influence of the sun’s rays.”
—Henry David Thoreau (1817–1862)
“You treat world history as a mathematician does mathematics, in which nothing but laws and formulas exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.”
—Hermann Hesse (1877–1962)