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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.
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 ...
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.
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In traditional logic, a particular negative categorical proposition, stating that some members of the subject class are not members of the predicate class. [2] [218] or A logical connective (disjunction) that links propositions in a way that the compound proposition is true if at least one of the linked propositions is true. ordered logic
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 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