Representing Knowledge and Querying Data using Double-Functorial Semantics
Michael Lambert (University of Massachusetts-Boston), Evan Patterson (Topos Institute)
分类理论为知识表示和数据库系统提供了数学基础。 流行的现有方法将数据库实例建模为集合和函数的类别,或作为2个functor进入集合,关系和影响的2类。 功能和关系模型由双函子统一为集、功能、关系和影响的双重类别。 在可访问的,示例驱动的风格中,我们表明“关系双重类别”的抽象结构是一种灵活而富有表现力的语言,其中可以代表知识,我们展示了如何以Codd的关系代数的精神对数据的查询如何被双重功能语义捕获。
Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the category of sets and functions, or as a 2-functor into the 2-category of sets, relations, and implications. The functional and relational models are unified by double functors into the double category of sets, functions, relations, and implications. In an accessible, example-driven style, we show that the abstract structur...
