Formal Concept Analysis with Many-sorted Attributes

TL;DR

This paper integrates constraint-based reasoning with formal concept analysis using distributed relations to reveal semantic structures in many-sorted attribute networks, advancing theoretical understanding in both areas.

Contribution

It introduces distributed relations as a semantic extension to formal contexts, uniting two distinct problem-solving traditions in computer science.

Findings

Distributed relations serve as a many-sorted extension to formal contexts.

Formal concept analysis can uncover semantic structures in distributed relations.

The approach bridges constraint networks and formal concept analysis.

Abstract

This paper unites two problem-solving traditions in computer science: (1) constraint-based reasoning, and (2) formal concept analysis. For basic definitions and properties of networks of constraints, we follow the foundational approach of Montanari and Rossi. This paper advocates distributed relations as a more semantic version of networks of constraints. The theory developed here uses the theory of formal concept analysis, pioneered by Rudolf Wille and his colleagues, as a key for unlocking the hidden semantic structure within distributed relations. Conversely, this paper offers distributed relations as a seamless many-sorted extension to the formal contexts of formal concept analysis. Some of the intuitions underlying our approach were discussed in a preliminary fashion by Freuder and Wallace.