Quantification in Double-Categorical Database Schemas

Abstract: The introduction of right adjoints to substitution in the equipment structure of a double olog allows modeling of relational division, an advanced query used in relational databases, for example, to compare a shopping list against an inventory. This talk with review relational division and show how it can be captured using these right adjoints in double-categorical database schemas. Asking for these adjoints enriches these structures in other ways. For example, such double ologs model full first-order modal logic, and thus description logic, and allow compound database queries involving disjunction, implication and negation. Beck-Chevalley and Frobenius Reciprocity are automatically satisfied in any such database schema and can be seen to be query optimization rules that are thus provably error-free.

category theory

Audience: researchers in the topic

Third Virtual Workshop on Double Categories