Let C 2 p denote the class of rst order sentences with two variables and with additional quantiiers \there exists exactly (at most, at least) i", for i p, and let C 2 be the union of C 2 p taken overâ€¦ (More)

We analyse the complexity of finite model reasoning in the description logicALCQI , i.e.,ALC augmented with qualifying number restrictions, inverse roles, and general TBoxes. It turns out that allâ€¦ (More)

We show that every finitely satisfiable two-variable first-order formula with two equivalence relations has a model of size at most triply exponential with respect to its length. Thus the finiteâ€¦ (More)

We consider the satisfiability and finite satisfiability problems for extensions of the two-variable fragment of first-order logic in which an equivalence closure operator can be applied to a fixedâ€¦ (More)

We show that the satisfiability problem for the two-variable first-order logic, FO2, over transitive structures when only one relation is required to be transitive, is decidable. The result isâ€¦ (More)