Towards arrow-theoretic semantics of ontologies: conceptories

TL;DR

This paper introduces conceptories, a new category-theoretic framework for knowledge representation, proposing their use as expressive alternatives to traditional limits and exploring their potential for formal ontological systems.

Contribution

It proposes the conceptory framework, integrating category-theoretic and logical methods for ontologies, and discusses their formal development and applications.

Findings

Conceptories serve as expressive alternatives to (co)limits.

They exhibit features similar to (pro-, in-)jections.

Potential applications to formal ontological systems.

Abstract

In context of efforts of composing category-theoretic and logical methods in the area of knowledge representation we propose the notion of conceptory. We consider intersection/union and other constructions in conceptories as expressive alternative to category-theoretic (co)limits and show they have features similar to (pro-, in-)jections. Then we briefly discuss approaches to development of formal systems built on the base of conceptories and describe possible application of such system to the specific ontology.