Meta-Modelling in Formal Concept Analysis
Yingjian Wang
TL;DR
The paper addresses extending Formal Concept Analysis to meta-modelling by introducing Triadic Concept Analysis to handle meta-attributes and ternary relations. It develops a framework to construct triadic contexts from two dyadic contexts, and discusses isomorphisms with dyadic concept lattices alongside triadic and conditional implications, complemented by visualizations. Formal definitions, derivation-based concepts, and lattice-based reasoning are provided to enable structured analysis of meta-attributes within FCA. This work offers a principled approach to representing and reasoning about attributes of attributes, with practical visualization and theoretical connections to standard FCA lattices.
Abstract
Formal Concept Analysis starts from a very basic data structure comprising objects and their attributes. Sometimes, however, it is beneficial to also define attributes of attributes, viz., meta-attributes. In this paper, we use Triadic Formal Concept Analysis, a triadic approach to Formal Concept Analysis, to develop a framework for this kind of meta-modelling in Formal Concept Analysis, including formal definitions and appropriate visualizations.