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)
“Those who guard their mouths preserve their lives; those who open wide their lips come to ruin.”
—Bible: Hebrew, Proverbs 13:3.
“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)