2015/03/28 by Marco A. Pérez, David I. Spivak, Pérez, Marco A. +1
Agricultural and Biological Sciences · Mathematics · #Category Theory (math.CT) #Cephalopods and Marine Biology #FOS: Mathematics #math.CT
paper · pdf · doi:10.48550/arxiv.1503.08326
35 pages. There are several improvements with respect to the previous version: (1) many concepts where redefined in order to provide a more formal description of ontology logs, via the use of bicategories, lax functors and lax transformations, (2) all proofs are now given as prose arguments, merged with the text
openalex publication_date 2015/03/28 · arxiv created 2015/06/22 · arxiv updated 2015/06/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 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 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.