Complexity of learning in concept lattices from positive and negative examples Original Research Article

A model of learning from positive and negative examples in concept lattices is considered. Lattice- and graph-theoretic interpretations of learning concept-based classification rules (called hypotheses) and classification in this model are given. The problems of counting all formal concepts, all hypotheses, and all minimal hypotheses are shown to be #P-complete. NP-completeness of some decision problems related to learning and classification in this setting is demonstrated and several conditions of tractability of these problems are considered. Some useful particular cases where these problems can be solved in polynomial time are indicated.