Abstract The main motivation for this work is the open question of decidability of the satisfiability problem for the two-variable fragment of first-order logic, ${\mathcal{FO}^{2}}$, with one transitive relation. In the presence of equality, the problem can be reduced to the corresponding problem when the transitive relation is required to be a strict partial order. It is known that its finite satisfiability problem is decidable but the decidability of the general satisfiability problem has been resolved only for restricted variants. More precisely, the problem is decidable for the fragment with comparable witnesses in which existential quantifiers are required to be guarded by atoms of the form $x

We present an algorithm for solving the unification problem in the description logic FL_bottom. This logic extends FL_0 with the bottom constructor and thus supports conjunction, value restrictions, top and bottom. Unification of concepts may become a useful tool for ontology maintenance; however, little is known about unification even in small, restricted description logics. The unification problem has been solved only for FL_0 and EL. This paper contributes to the ongoing effort to extend these results to richer logics. Our algorithm runs in exponential time with respect to the size of the problem.