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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 .
Note that the last one (carry the piano together) can be made non-collective by removing the word together. Quantifiers differ with respect to whether or not they can be the subject of a collective predicate. For example, quantifiers formed with all the can, while ones formed with every or each cannot. All the students formed a line.
Example requires a quantifier over predicates, which cannot be implemented in single-sorted first-order logic: Zj → ∃X(Xj∧Xp). Quantification over properties Santa Claus has all the attributes of a sadist. Example requires quantifiers over predicates, which cannot be implemented in single-sorted first-order logic: ∀X(∀x(Sx → Xx) → ...
A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variables’ value or values. In propositional logic, atomic formulas are sometimes regarded as zero-place predicates. [1] In a sense, these are nullary (i.e. 0-arity) predicates.
existential quantifier A quantifier used in predicate logic to indicate that there exists at least one member of the domain for which the predicate holds true. existential variable A variable in predicate logic that is bound by an existential quantifier, representing an unspecified member of the domain that satisfies the predicate. [129] [130]
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 ...
Two important types of logical constants are logical connectives and quantifiers. The equality predicate (usually written '=') is also treated as a logical constant in many systems of logic . One of the fundamental questions in the philosophy of logic is "What is a logical constant?"; [ 1 ] that is, what special feature of certain constants ...
In other words, an operator has scope of operation, or affecting the interpretation of other phrases, only within its own domain. Three uncontroversial examples of scope affecting some aspect of the interpretation are: quantifier-quantifier, quantifier-pronoun, quantifier-negative polarity item.
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