Search results
Results From The WOW.Com Content Network
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier ∀ {\displaystyle \forall } in the first order formula ∀ x P ( x ) {\displaystyle \forall xP(x)} expresses that everything in the domain satisfies the property denoted by P ...
The theory of real closed fields is the theory in which the primitive operations are multiplication and addition; this implies that, in this theory, the only numbers that can be defined are the real algebraic numbers. As proven by Tarski, this theory is decidable; see Tarski–Seidenberg theorem and Quantifier elimination.
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier (" ∃x" or "∃(x)" or ...
In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", or "for any". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation to every member of the domain.
In mathematical logic, a Lindström quantifier is a generalized polyadic quantifier. Lindström quantifiers generalize first-order quantifiers, such as the existential quantifier , the universal quantifier , and the counting quantifiers .
For example, the quantifier ∀ A, which can be viewed as set-theoretic inclusion, satisfies all of the above except [symmetry]. Clearly [symmetry] holds for ∃ A while e.g. [contraposition] fails. A semantic interpretation of conditional quantifiers involves a relation between sets of subsets of a given structure—i.e. a relation between ...
For each possible quantifier prefix to the prenex normal form, we have a fragment of first-order logic. For example, the Bernays–Schönfinkel class, [] =, is the class of first-order formulas with quantifier prefix , equality symbols, and no function symbols.
In computational complexity theory, the language TQBF is a formal language consisting of the true quantified Boolean formulas.A (fully) quantified Boolean formula is a formula in quantified propositional logic (also known as Second-order propositional logic) where every variable is quantified (or bound), using either existential or universal quantifiers, at the beginning of the sentence.