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...

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...

In mathematical logic, a theory is categorical if it has exactly one model (up to isomorphism). Such a theory can be viewed as defining its model, uniquely...

In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication...

Categorical theory, in mathematical logic Morley's categoricity theorem, a mathematical theorem in model theory Categorical data analysis Categorical...

logic more accessible. While his Latin translation of Prior Analytics went primarily unused before the 12th century, his textbooks on the categorical...

as a consequence of combining the concept of sheaf and closure under categorical operations. It plays a certain definite role in cohomology theories....

corresponds to the conjunction ∧ {\displaystyle \land } of predicates. In categorical logic, a subfield of topos theory, quantifiers are identified with adjoints...

and includes the study of categorical logic, but category theory is not ordinarily considered a subfield of mathematical logic. Because of its applicability...

to Philosophical Logic. Blackwell, ISBN 0-631-20693-0 Lambek, J. and Scott, P. J., 1986. Introduction to Higher Order Categorical Logic, Cambridge University...

to both analogical reasoning and categorical syllogism in a real sense. The first original Arabic writings on logic were produced by al-Kindi (Alkindus)...

Noncommutative geometry Categorical algebra Grothendieck's Galois theory Grothendieck topology Topological dynamics Categorical dynamics Crossed module...

In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to...

"All men are mortal" and "Socrates is a man." Aristotelian logic identifies a categorical proposition as a sentence which affirms or denies a predicate...

such as pointless topology. Categorical logic is now a well-defined field based on type theory for intuitionistic logics, with applications in functional...

turn leads to categorical logic because a logic over a type theory categorically corresponds to one ("total") category, capturing the logic, being fibred...

Syntax (logic) Truth Truth value Validity Affine logic Alethic logic Aristotelian logic Boolean logic Buddhist logic Bunched logic Categorical logic Classical...

Universal Logic is an emerging interdisciplinary field involving logic, non-classical logic, categorical logic, set theory, foundation of logic, and the...

branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. Sometimes...

2019, 6. Categorical Syllogisms. Hurley 2015, 4. Categorical Syllogisms. Spriggs 2012, pp. 20–22. Hintikka 2019, §Nature and varieties of logic, §Alternative...

portal Categorical logic First-order logic § Many-sorted logic Carlos Caleiro, Ricardo Gonçalves (2006). "On the algebraization of many-sorted logics". Proc...

mathematician William Lawvere) is a category that can be considered a categorical counterpart of the notion of an equational theory. Let ℵ 0 {\displaystyle...

structures, i.e. categorical axiom systems, can be obtained in stronger logics such as second-order logic. The foundations of first-order logic were developed...

Impredicative Definable real number Algebraic logic Boolean algebra (logic) Dialectica space categorical logic Finite model theory Descriptive complexity...

Sam will meet Jack at the movies." In traditional logic, where there are four named types of categorical propositions, only forms A (i.e., "All S are P")...

(2001). "The Development of Categorical Logic". In Gabbay, D.M.; Guenthner, Franz (eds.). Handbook of Philosophical Logic. Vol. 12 (2nd ed.). Springer...

algebraic topology, categorical topology, quantum topology, low-dimensional topology; Categorical logic and set theory in the categorical context such as...

lectures on categorical dynamics were a further step toward topos theory and his CUNY lectures on hyperdoctrines advanced categorical logic especially...

logic, the process of contraposition is a schema composed of several steps of inference involving categorical propositions and classes. A categorical...

Default logic is a non-monotonic logic proposed by Raymond Reiter to formalize reasoning with default assumptions. Default logic can express facts like...