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 ...
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.
First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables.
For example, adding a "there exist finitely many" quantifier results in a loss of compactness, whereas adding a "there exist uncountably many" quantifier to first-order logic results in a logic no longer satisfying the Löwenheim–Skolem theorem.
In semantics and mathematical logic, a quantifier is a way that an argument claims that an object with a certain property exists or that no object with a certain property exists. Not to be confused with Category:Quantification (science) .
In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition. [1] This sort of quantification is known as uniqueness quantification or unique existential quantification, and is often denoted with the symbols "∃!" [2] or "∃ =1". For example, the formal statement
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.
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 ...