Abstract Skew Hilbert algebras were recently introduced as a tool for a unified treatment of several ordered algebraic structures with implication important for mathematical logic. They were presented axiomatically as posets with implication, one of the axioms being stated in terms of lower and upper cones. In the paper, the important subclass of the so-called strong skew Hilbert algebras is shown to coincide with a class of weak BCK*-algebras that is axiomatized by simple quasi-equations. Several applications of skew Hilbert algebras are reconsidered in the context of weak BCK*-algebras, and the relevant classes of positive implicative and orthoimplicative weak BCK*-algebras are briefly reviewed.

Study of the so called knowledge ordering of rough sets was initiated by V.W. Marek and M. Truszczynski at the end of 90-ies. Under this ordering, the rough sets of a fixed approximation space form a domain in which every set ↓ is a Boolean algebra. In the paper, an additional operation inversion on rough set domains is introduced and an abstract axiomatic description of obtained algebras of rough set is given. It is shown that the resulting class of algebras is essentially different from those traditional in rough set theory: it is not definable, for instance, in the class of regular double Stone algebras, and conversely.