Concept Lattices of a Relational Structure

摘要

Conceptual patterns can be described by graphs, entailment by graph homomorphism. The mapping of a pattern to its set of instantiations, represented as a table, constitutes one half of a Galois connection. The join operation is the infimum in a complete lattice of tables, and a most descriptive pattern can be assigned to each table by means of a categorial product construction. This construction constitutes the other half of the Galois connection. In this approach, relational structures assume the role of formal contexts in standard Formal Concept Analysis (FCA). Concepts arise as connected components of powers of these relational structures. The ordered set of these concepts may be conceived as a navigation space.