A Triadic Approach to Formal Concept Analysis

Abstract. Formal Concept Analysis, developed uring the last fifteen years, has been based on the dyadic understanding of a concept con-stituted by its extension and its intension. The pragmatic philosophy of Charles S. Peirce with his three universal categories, and experiences in data analysis, have suggested a triadic approach to Formal Concept Analysis. This approach starts with the primitive notion of a triadic con-text defined as a quadruple (G, M, B, Y) where G, M, and B are sets and Y is a ternary relation between G, M, and B, i.e. Y C _ G • M • B; the elements of G, M, and B are called objects, attributes, and conditions, respectively, and (g, m, b) E Y is read: the object g has the attribute m under (or according to) the condition b. A triadic conceptof a triadic con-text (G, M, B, Y) is defined as a triple (A1, A2, A3) with A ~ • • C Y which is maximal with respect o component-wise inclusion. The triadic concepts are structured by three quasiorders given by the inclusion or-der within each of the three components. In analogy to the dyadic case