Description Logic for Rough Concepts

Rough concepts have been introduced in [7] in the context of a mathematical framework unifying Rough Set Theory (RST) and Formal Concept Analysis (FCA). Algebraically, the lower and upper approximation operators on a concept lattice have similar order-theoretic properties to the □ and ◊ operators in modal logic. Thus, the logic of rough concepts has been defined as a (non-distributive) lattice-based modal logic whose relational semantics consists of formal contexts enriched with relations (interpreting the modal operators) satisfying the axioms classically corresponding to the reflexivity, symmetry, and transitivity of the accessibility relations of Kripke frames. Recently, the description logic LE-ALC was introduced for reasoning in the semantic environment of these enriched formal contexts, and a tableaux algorithm was developed for checking the consistency of knowledge bases with acyclic TBoxes [5]. In the present paper, we introduce the description logic of rough concepts LE-ALCR, which extends LE-ALC with the (modal) axioms classically corresponding to reflexivity, symmetry, and transitivity, and develop its corresponding tableaux algorithm. We then introduce two extensions of LE-ALCR: the first one (LE-ALCRO) extending LE-ALCR with generated concepts, and the second one (LE-ALCRN) extending LE-ALCR with feature-pair inconsistencies. The resulting description logic is a framework for modeling reasoning problems related to rough concepts, which is demonstrated through the case-study of a knowledge base for Whittaker’s five kingdom classification of living things.