ALC for CLA: Towards description logic on concept lattices

In this paper, we start with a motivation of the study of modal and/or description logics with values in concept lattices. Then we give a brief survey of approaches to lattice-valued modal and/or description logics. After that we study some methods of context symmetrization, because in our approach the description logic on concept lattices is defined for symmetric contexts only. We conclude with a list of problems related to the comparison of different lattice-valued modal and/or description logics, different variants of context symmetrization and resulting description logics, decidability and axiomatization of these logics.