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Each kind of quantification defines a corresponding closure operator on the set of formulas, by adding, for each free variable x, a quantifier to bind x. [9] For example, the existential closure of the open formula n >2 ∧ x n + y n = z n is the closed formula ∃ n ∃ x ∃ y ∃ z ( n >2 ∧ x n + y n = z n ); the latter formula, when ...
A counting quantifier is a mathematical term for a quantifier of the form "there exists at least k elements that satisfy property X". In first-order logic with equality, counting quantifiers can be defined in terms of ordinary quantifiers, so in this context they are a notational shorthand.
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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.
Some of the details can be found in the article Lindström quantifier. Conditional quantifiers are meant to capture certain properties concerning conditional reasoning at an abstract level. Generally, it is intended to clarify the role of conditionals in a first-order language as they relate to other connectives, such as conjunction or ...
Lindström quantifiers generalize first-order quantifiers, such as the existential quantifier, the universal quantifier, and the counting quantifiers. They were introduced by Per Lindström in 1966. They were later studied for their applications in logic in computer science and database query languages .
Filter quantifiers are a type of logical quantifier which, informally, say whether or not a statement is true for "most" elements of . Such quantifiers are often used in combinatorics , model theory (such as when dealing with ultraproducts ), and in other fields of mathematical logic where (ultra)filters are used.
The first-order quantifiers are not restricted. By analogy to Fagin's theorem , according to which existential (non-monadic) second-order logic captures precisely the descriptive complexity of the complexity class NP , the class of problems that may be expressed in existential monadic second-order logic has been called monadic NP.