Ologs: a categorical framework for knowledge representation

TL;DR

This paper introduces ologs, a category-theoretic framework for knowledge representation that is mathematically rigorous, user-friendly, and capable of modeling complex information and functions.

Contribution

It presents ologs as a novel, formal, and accessible approach to knowledge representation, bridging category theory and practical data modeling.

Findings

Ologs can describe any primitive recursive function.

Ologs are comparable to relational database schemas but easier to author.

Ologs can be connected into networks for integrated knowledge systems.

Abstract

In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relational database schema; in fact an olog can serve as a data repository if desired. Unlike database schemas, which are generally difficult to create or modify, ologs are designed to be user-friendly enough that authoring or reconfiguring an olog is a matter of course rather than a difficult chore. It is hoped that learning to author ologs is much simpler than learning a database definition language, despite their similarity. We describe ologs carefully and illustrate with many examples. As an application we show that any primitive recursive function can be described by an olog. We also show that ologs can be aligned or connected together into a larger network using functors. The various methods of information flow and institutions can then be used to integrate local and global world-views. We finish by providing several different avenues for future research.