Categorial Graphs

In this paper we present a denotational semantics for a class of database definition languages. We present a language, called categorial graph language, that combines both graphical and textual phrases and is tailored to define databases. The categorial graph language is modeled after a number of practical languages. Its semantics is based on a variant of linear logic, and incorporates directly the notions expressed in the language. We emphasize on the fact that in the semantics presented here, we directly axiomatize the behavior of complex objects, instead of encoding it with help of the traditional mathematical notions. We will argue that this is desirable regarding clearness of semantics and matters of complexity.