Distributed Conceptual Structures (1810.04774v1)

Abstract: The theory of distributed conceptual structures, as outlined in this paper, is concerned with the distribution and conception of knowledge. It rests upon two related theories, Information Flow and Formal Concept Analysis, which it seeks to unify. Information Flow (IF) is concerned with the distribution of knowledge. The foundations of Information Flow is explicitly based upon a mathematical theory known as the Chu Construction in *-autonomous categories and implicitly based upon the mathematics of closed categories. Formal Concept Analysis (FCA) is concerned with the conception and analysis of knowledge. In this paper we connect these two studies by extending the basic theorem of Formal Concept Analysis to the distributed realm of Information Flow. The main results are the categorical equivalence between classifications and concept lattices at the level of functions, and the categorical equivalence between bonds and complete adjoints at the level of relations. With this we hope to accomplish a rapprochement between Information Flow and Formal Concept Analysis.