Monoidal Categories for Formal Concept Analysis

TL;DR

This paper explores monoidal categories in formal concept analysis, revealing new structures and their potential for compositional models of meaning, linking formal contexts with lattice theory.

Contribution

It introduces a second monoidal structure on categories of formal contexts, connecting formal concept analysis with monoidal category theory and compositional semantics.

Findings

Existence of a second monoidal structure on categories of formal contexts

Equivalence between bonds/Chu correspondences and *-autonomous categories

Potential application in compositional models of meaning

Abstract

We investigate monoidal categories of formal contexts, in which states correspond to formal concepts. In particular we examine the category of bonds or Chu correspondences between contexts, which is known to be equivalent to the *-autonomous category of complete sup-lattices. We show that a second monoidal structure exists on both categories, corresponding to the direct product of formal contexts defined by Ganter and Wille, and discuss the use of these categories as compositional models of meaning.