In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor. The categorical framework provides a rich conceptual background for …

Dec 27, 2025 · There are only two mathematically distinct valid categorical syllogisms. The other valid categorical syllogisms can be converted to these—or derived from these—by applying identities from …

Our categorical logic research applies category theory to connect syntax and semantics, developing new logical systems like homotopy type theory with intrinsic geometric content for formal verification.

Dec 6, 1996 · On the other hand, philosophers and philosophical logicians can employ category theory and categorical logic to explore philosophical and logical problems. I now discuss these challenges, …

Categorical logic is a fairly simple logic of categories or classes. A class is a group of things that we designate with a common noun: students, teachers, dogs, politicians, etc.

The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over …

In Logic, this is known as the study of Categorical Propositions, i.e., statements which assert something about membership between two categories of things. There are four standard form categorical …

For instance, the dualities of Stone, Lawvere, and Makkai that spurred the early devel-opment of categorical logic now fall into place from the standpoint shown in table 1, that focuses on typing, …

Dec 21, 2017 · A branch of mathematics dealing with the interaction between logic (cf. also Mathematical logic) and category theory. Each of these disciplines has profoundly influenced the other.

“Category” is just a synonym of “class.” Categorical propositions are propositions that make a claim about the relationship between two classes. This is the first step in taming natural language: …