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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 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.
List of mathematical logic topics; There is a list of paradoxes on the paradox page. There is a list of fallacies on the logical fallacy page. Modern mathematical logic is at the list of mathematical logic topics page. For introductory set theory and other supporting material see the list of basic discrete mathematics topics
intensional logic A logic that deals with the intensional aspects of meaning, such as belief, necessity, and possibility, distinguishing between logically equivalent expressions that have different modal properties. intermediate logic
Journal of Logic and Analysis, 2009 ff. (Successor of Logic and Analysis). Journal of Logic and Computation, Oxford 1990 ff. Journal of Logic, Language and Information, 1992 ff. Journal of Logic Programming, (Elsevir Publ.) 1984–2000. Continued by Theory and Practice of Logic Programming and The Journal of Logic and Algebraic Programming ...
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.
An intensional statement-form is a statement-form with at least one instance such that substituting co-extensive expressions into it does not always preserve logical value. An intensional statement is a statement that is an instance of an intensional statement-form.
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.