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 in the first order formula () expresses that everything in the domain satisfies the property denoted by .
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.
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [ 1 ] and the LaTeX symbol.
In standard semantics, also called full semantics, the quantifiers range over all sets or functions of the appropriate sort. A model with this condition is called a full model, and these are the same as models in which the range of the second-order quantifiers is the powerset of the model's first-order part. [3]
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 ...
Along with numerals, and special-purpose words like some, any, much, more, every, and all, they are quantifiers. Quantifiers are a kind of determiner and occur in many constructions with other determiners, like articles: e.g., two dozen or more than a score. Scientific non-numerical quantities are represented as SI units.
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.
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.