  W.C. Rounds and G.-Q. Zhang (2001) have proposed to study a form of
disjunctive logic programming generalized to algebraic domains. This system
allows reasoning with information which is hierarchically structured and forms
a (suitable) domain. We extend this framework to include reasoning with default
negation, giving rise to a new nonmonotonic reasoning framework on hierarchical
knowledge which encompasses answer set programming with extended disjunctive
logic programs. We also show that the hierarchically structured knowledge on
which programming in this paradigm can be done, arises very naturally from
formal concept analysis. Together, we obtain a default reasoning paradigm for
conceptual knowledge which is in accordance with mainstream developments in
nonmonotonic reasoning.
