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Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science. [1] In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor.
In mathematical logic, a theory is categorical if it has exactly one model (up to isomorphism). [a] Such a theory can be viewed as defining its model, uniquely characterizing the model's structure. In first-order logic, only theories with a finite model can be categorical. Higher-order logic contains categorical theories with an infinite model.
In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the subject term) are included in another (the predicate term). [1]
Categorical logic is now a well-defined field based on type theory for intuitionistic logics, with applications in functional programming and domain theory, where a cartesian closed category is taken as a non-syntactic description of a lambda calculus.
In syllogistic logic, there are 256 possible ways to construct categorical syllogisms using the A, E, I, and O statement forms in the square of opposition. Of the 256, only 24 are valid forms. Of the 24 valid forms, 15 are unconditionally valid, and 9 are conditionally valid.
In traditional logic, a proposition (Latin: propositio) is a spoken assertion (oratio enunciativa), not the meaning of an assertion, as in modern philosophy of language and logic. A categorical proposition is a simple proposition containing two terms, subject (S) and predicate (P), in which the predicate is either asserted or denied of the subject.
categorical logic A branch of logic that studies the categorization of objects and the logical foundations of categories, often using the framework of category theory. categorical proposition A proposition that asserts or denies that all or some of the members of one category are included in another category, fundamental in syllogistic reasoning.
Pages in category "Categorical logic" The following 7 pages are in this category, out of 7 total. This list may not reflect recent changes. ...