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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.
Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe , by additional quantifiers that range over terms that may have such individuals as their value .
Transparent intensional logic (frequently abbreviated as TIL) is a logical system created by Pavel Tichý. Due to its rich procedural semantics TIL is in particular apt for the logical analysis of natural language. From the formal point of view, TIL is a hyperintensional, partial, typed lambda calculus.
He worked in the field of intensional logic and founded transparent intensional logic, an original theory of the logical analysis of natural languages – the theory is devoted to the problem of saying exactly what it is that we learn, know and can communicate when we come to understand what a sentence means. He spent roughly 25 years working ...
In philosophical logic, the masked-man fallacy (also known as the intensional fallacy or epistemic fallacy) [1] is committed when one makes an illicit use of Leibniz's law in an argument. Leibniz's law states that if A and B are the same object, then A and B are indiscernible (that is, they have all the same properties).
Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory (MLTT)) is a type theory and an alternative foundation of mathematics. Intuitionistic type theory was created by Per Martin-Löf , a Swedish mathematician and philosopher , who first published it in 1972.
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.
The first higher-dimensional models of intensional type theory were constructed by Steve Awodey and his student Michael Warren in 2005 using Quillen model categories.These results were first presented in public at the conference FMCS 2006 [5] at which Warren gave a talk titled "Homotopy models of intensional type theory", which also served as his thesis prospectus (the dissertation committee ...