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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.
Pages in category "Categorical logic" The following 7 pages are in this category, out of 7 total. This list may not reflect recent changes. ...
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]
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.
Founds categorical logic, discovers internal logics of categories and recognizes its importance and introduces Lawvere theories. Essentially categorical logic is a lift of different logics to being internal logics of categories. Each kind of category with extra structure corresponds to a system of logic with its own inference rules.
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.
Categorical may refer to: Categorical imperative, a concept in philosophy developed by Immanuel Kant; Categorical theory, in mathematical logic; Morley's categoricity theorem, a mathematical theorem in model theory; Categorical data analysis; Categorical distribution, a probability distribution
categorical logic Categorical logic is an approach to mathematical logic that uses category theory. categorical probability categorical probability categorification categorification is a process of replacing sets and set-theoretic concepts with categories and category-theoretic concepts in some nontrivial way to capture categoric flavors ...