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  2. Quantifier (logic) - Wikipedia

    en.wikipedia.org/wiki/Quantifier_(logic)

    As an example, the only difference in the definition of uniform continuity and (ordinary) continuity is the order of quantifications. First order quantifiers approximate the meanings of some natural language quantifiers such as "some" and "all". However, many natural language quantifiers can only be analyzed in terms of generalized quantifiers.

  3. Predicate functor logic - Wikipedia

    en.wikipedia.org/wiki/Predicate_functor_logic

    Translate the matrices of the most deeply nested quantifiers into disjunctive normal form, consisting of disjuncts of conjuncts of terms, negating atomic terms as required. The resulting subformula contains only negation, conjunction, disjunction, and existential quantification.

  4. Von Neumann–Bernays–Gödel set theory - Wikipedia

    en.wikipedia.org/wiki/Von_Neumann–Bernays...

    Bound variables within nested quantifiers are handled by increasing the subscript by one for each successive quantifier. This leads to rule 4, which must be applied after the other rules since rules 1 and 2 produce quantified variables.

  5. Non-numerical words for quantities - Wikipedia

    en.wikipedia.org/wiki/Non-numerical_words_for...

    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.

  6. Mathematical logic - Wikipedia

    en.wikipedia.org/wiki/Mathematical_logic

    In this logic, quantifiers may only be nested to finite depths, as in first-order logic, but formulas may have finite or countably infinite conjunctions and disjunctions within them. Thus, for example, it is possible to say that an object is a whole number using a formula of L ω 1 , ω {\displaystyle L_{\omega _{1},\omega }} such as

  7. Higher-order logic - Wikipedia

    en.wikipedia.org/wiki/Higher-order_logic

    In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expressive, but their model-theoretic properties are less well-behaved than those of first-order ...

  8. First-order logic - Wikipedia

    en.wikipedia.org/wiki/First-order_logic

    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) → ...

  9. Conditional quantifier - Wikipedia

    en.wikipedia.org/wiki/Conditional_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 disjunction.