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:
“It is now time to stop and to ask ourselves the question which my last commanding officer, Admiral Hyman Rickover, asked me and every other young naval officer who serves or has served in an atomic submarine. For our Nation M for all of us M that question is, “Why not the best?””
—Jimmy Carter (James Earl Carter, Jr.)
“Rain falls into the open eyes of the dead
Again again with its pointless sound
When the moon finds them they are the color of everything”
—William Stanley Merwin (b. 1927)
“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)