Toward formalizing ologs: Linguistic structures, instantiations, and mappings

TL;DR

This paper formalizes the concept of ologs using linguistic structures on categories, introducing bicategories and functors to better understand ontology logs and their relation to databases.

Contribution

It develops a formal framework for ologs based on linguistic structures, bicategories, and new functor notions, extending prior categorical approaches.

Findings

Defined a bicategory of English phrases endorsed as functional

Introduced a new notion of linguistic functor extending meaningful functors

Discussed the relationship between ologs and databases

Abstract

We define the notion of linguistic structure on a small category, in order to provide a more formal description of ontology logs, also known as ologs, introduced by R. E. Kent and D. I. Spivak in their paper "Ologs: A categorical framework for knowledge representation." In particular, we construct a bicategory $\mathsf{Eng}$, of English noun phrases and verb phrases, endorsed as functional by varying sets of authors. An olog is then defined as a lax functor to $\mathsf{Eng}$. We then present a new notion of linguistic functor, which extends Spivak's notion of meaningful functors. Finally, we discuss the relationship between ologs and databases in this context.