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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 logic, a categorical proposition, ... English Sentence ... This is because the translation to natural language is ambiguous. In common speech, the sentence "All ...
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 ...
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.
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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 grammar for this language can be found in Vijay-Shanker and Weir (1994). [ 1 ] Vijay-Shanker and Weir (1994) [ 1 ] demonstrates that Linear Indexed Grammars , Combinatory Categorial Grammars, Tree-adjoining Grammars , and Head Grammars are weakly equivalent formalisms, in that they all define the same string languages.
This calculus is a forerunner of linear logic in that it is a substructural logic. Montague grammar is based on the same principles as categorial grammar. [ 2 ] Montague's work helped to bolster interest in categorial grammar by associating it with his highly successful formal treatment of natural language semantics .