Formal Definition
The precise semantic interpretation of an atomic formula and an atomic sentence will vary from theory to theory.
- In propositional logic, atomic formulae are called propositional variables. In a sense, these are nullary (i.e. 0-arity) predicates.
- In first-order logic, an atomic formula consists of a predicate symbol applied to an appropriate number of terms.
- In set theory, predicates are understood to be characteristic functions or set indicator functions, i.e. functions from a set element to a truth value. Set-builder notation makes use of predicates to define sets.
- In autoepistemic logic, which rejects the law of excluded middle, predicates may be true, false, or simply unknown; i.e. a given collection of facts may be insufficient to determine the truth or falsehood of a predicate.
- In fuzzy logic, predicates are the characteristic functions of a probability distribution. That is, the strict true/false valuation of the predicate is replaced by a quantity interpreted as the degree of truth.
Read more about this topic: Predicate (mathematical Logic)
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