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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 .
An intensional definition may also consist of rules or sets of axioms that define a set by describing a procedure for generating all of its members. For example, an intensional definition of square number can be "any number that can be expressed as some integer multiplied by itself". The rule—"take an integer and multiply it by itself ...
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).
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.
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 ...
A close friend of the logician Pavel Tichý, he was a keen follower and developer of Tichý's transparent intensional logic (TIL): Based on the procedural semantics of TIL, I developed a new and original theory of concepts, where concept is a closed TIL construction.
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.