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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. ...
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
A theory is κ-categorical (or categorical in κ) if it has exactly one model of cardinality κ up to isomorphism. Morley's categoricity theorem is a theorem of Michael D. Morley ( 1965 ) stating that if a first-order theory in a countable language is categorical in some uncountable cardinality , then it is categorical in all uncountable ...
Outside that field, it has been influential particularly on category theory and categorical logic. In the usual formulation, the point of view treats not objects X of a given category C, but morphisms. f: X → S. where S is a fixed object. This idea is made formal in the idea of the slice category of objects of C 'above' S.
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.
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.
Video archive of recorded talks relevant to categories, logic and the foundations of physics. Interactive Web page which generates examples of categorical constructions in the category of finite sets. Category Theory for the Sciences, an instruction on category theory as a tool throughout the sciences.