Atomic Formula
Jump to navigation
Jump to search
An Atomic Formula is a mathematical formula with no deeper propositional structure.
- Example(s):
- Counter-Example(s):
- See: Mathematical Logic, Logic Formula, Proposition, Logical Connective, Subformula, Well-Formed Formula, Propositional Logic, Propositional Variable, Predicate Logic, First-Order Logic, Model Theory, String (Computer Science), Signature (Logic).
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Atomic_formula Retrieved:2015-1-2.
- In mathematical logic, an atomic formula (also known simply as an atom) is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformulas. Atoms are thus the simplest well-formed formulas of the logic. Compound formulas are formed by combining the atomic formulas using the logical connectives.
The precise form of atomic formulas depends on the logic 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. In model theory, atomic formula are merely strings of symbols with a given signature, which may or may not be satisfiable with respect to a given model.
- In mathematical logic, an atomic formula (also known simply as an atom) is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformulas. Atoms are thus the simplest well-formed formulas of the logic. Compound formulas are formed by combining the atomic formulas using the logical connectives.
2009
- CYC Glossary http://www.cyc.com/cycdoc/ref/glossary.html
- QUOTE: atomic formula: An atomic formula is an expression in CycL of the following form: a list with opening and closing parentheses such that the first element of the list is a CycL predicate, and the remaining elements are the arguments to the predicate. Atomic formulas use no logical connectives. See also ground atomic formula. In CycL atomic formulas may have variables, constants, or other terms as arguments to the CycL predicate.