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An extensional definition gives meaning to a term by specifying its extension, that is, every object that falls under the definition of the term in question.. For example, an extensional definition of the term "nation of the world" might be given by listing all of the nations of the world, or by giving some other means of recognizing the members of the corresponding class.
Modal logic can be regarded also as the most simple appearance of such studies: it extends extensional logic just with a few sentential functors: [13] these are intensional, and they are interpreted (in the metarules of semantics) as quantifying over possible worlds. For example, the Necessity operator (the 'box') when applied to a sentence A ...
A language is intensional if it contains intensional statements, and extensional otherwise. All natural languages are intensional. [4] The only extensional languages are artificially constructed languages used in mathematical logic or for other special purposes and small fragments of natural languages.
These learning styles are not innate to an individual but rather are developed based on an individual's experiences and preferences. [10] Based on this model, the Honey and Mumford's Learning Styles Questionnaire (LSQ) [11] was developed to allow individuals to assess and reflect on how they consume information and learn from their experiences ...
Montague grammar is an approach to natural language semantics, named after American logician Richard Montague.The Montague grammar is based on mathematical logic, especially higher-order predicate logic and lambda calculus, and makes use of the notions of intensional logic, via Kripke models.
In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are implied ...
There are multiple versions of the type theory: Martin-Löf proposed both intensional and extensional variants of the theory and early impredicative versions, shown to be inconsistent by Girard's paradox, gave way to predicative versions. However, all versions keep the core design of constructive logic using dependent types.
The semantics is tailored to the hardest case, as constituted by hyperintensional contexts, and generalized from there to intensional and extensional contexts. The underlying logic is a Frege-style function/argument one, treating functions, rather than relations or sets, as primitive, together with a Church-style logic, centred on the ...