Toward formalizing ologs: Linguistic structures, instantiations, and mappings
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.
 Publication:

arXiv eprints
 Pub Date:
 March 2015
 arXiv:
 arXiv:1503.08326
 Bibcode:
 2015arXiv150308326P
 Keywords:

 Mathematics  Category Theory
 EPrint:
 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