Definition & Betydelse | Engelska ordet QUANTIFIERS

Definition av QUANTIFIERS

1. böjningsform av quantifier

Exempel på hur man kan använda QUANTIFIERS i en mening

• Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or quantifiers.
• Articles are part of a broader category called determiners, which also include demonstratives, possessive determiners, and quantifiers.
• In quantified modal logic, the Barcan formula and the converse Barcan formula (more accurately, schemata rather than formulas) (i) syntactically state principles of interchange between quantifiers and modalities; (ii) semantically state a relation between domains of possible worlds.
• Following Lévy's hierarchy, here one looks at formulas with m-1 alternations of quantifiers with the outermost quantifier being universal.
• Keisler proved that such a hyperreal definition of limit reduces the quantifier complexity by two quantifiers.
• An atomic formula is a formula that contains no logical connectives nor quantifiers, or equivalently a formula that has no strict subformulas.
• A formula of the predicate calculus is in prenex normal form (PNF) if it is written as a string of quantifiers and bound variables, called the prefix, followed by a quantifier-free part, called the matrix.
• It is notable that Skolem, like Löwenheim, wrote on mathematical logic and set theory employing the notation of his fellow pioneering model theorists Charles Sanders Peirce and Ernst Schröder, including Π, Σ as variable-binding quantifiers, in contrast to the notations of Peano, Principia Mathematica, and Principles of Mathematical Logic.
• He also observed that this idea is in a way just a natural extension of Richard Montague's approach in "The Proper Treatment of Quantification in Ordinary English" (PTQ), writing that "with the benefit of hindsight, a limited form of continuation-passing is clearly discernible at the core of Montague’s (1973) PTQ treatment of NPs as generalized quantifiers".
• In particular, Montague's influence lives on in grammar approaches like categorial grammar (such as Unification Categorial Grammar, Left-Associative Grammar, or Combinatory Categorial Grammar), which attempt a derivation of syntactic and semantic representation in tandem and the semantics of quantifiers, scope and discourse (Hans Kamp, a student of Montague's, co-developed Discourse Representation Theory).
• Its logical vocabulary has several sorts of conjunctions, disjunctions, quantifiers, implications, negations and so called recurrence operators.
• The ordinary axiomatization of second-order arithmetic uses a set-based language in which the set quantifiers can naturally be viewed as quantifying over Cantor space.
• the nonstandard definition of a concept is simpler than the standard definition (both intuitively simpler and simpler in a technical sense, such as quantifiers over lower types or fewer alternations of quantifiers).
• Lawvere's Chicago lectures on categorical dynamics were a further step toward topos theory and his CUNY lectures on hyperdoctrines advanced categorical logic especially using his 1963 discovery that existential and universal quantifiers can be characterized as special cases of adjoint functors.
• Frege presents his calculus using idiosyncratic two-dimensional notation: connectives and quantifiers are written using lines connecting formulas, rather than the symbols ¬, ∧, and ∀ in use today.
• The work begins by analyzing simple categoric propositions, and draws a series of basic conclusions on the routine issues of classifying and defining basic linguistic forms, such as simple terms and propositions, nouns and verbs, negation, the quantity of simple propositions (primitive roots of the quantifiers in modern symbolic logic), investigations on the excluded middle (which to Aristotle is not applicable to future tense propositions—the problem of future contingents), and on modal propositions.
• Since the sentences above each contain two quantifiers ('some' and 'every' in the first sentence and 'all' and 'at least one' in the second sentence), they cannot be adequately represented in TL.
• If predicate variables are also allowed to be bound to predicate letters which are unary or have higher arity, and when such letters represent propositional functions, such that the domain of the arguments is mapped to a range of different propositions, and when such variables can be bound by quantifiers to such sets of propositions, then the result is a higher-order predicate calculus, or higher-order logic.
• It was found that the connectives of pre-categorical logic were more clearly understood using the concept of adjoint functor, and that the quantifiers were also best understood using adjoint functors.
• SO-Krom is the set of boolean queries definable with second-order formulae in conjunctive normal form such that the first-order quantifiers are universal and the quantifier-free part of the formula is in Krom form, which means that the first-order formula is a conjunction of disjunctions, and in each "disjunction" there are at most two variables.

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