Satissability Problem in Description Logics with Modal Operators

The paper considers the standard concept description language ALC augmented with various kinds of modal operators which can be applied to concepts and axioms. The main aim is to develop methods of proving decid-ability of the satissability problem for this language and apply them to description logics with most important temporal and epis-temic operators, thereby obtaining satissa-bility checking algorithms for these logics. We deal with the possible world semantics under the constant domain assumption and show that the expanding and varying domain assumptions are reducible to it. Models with both nite and arbitrary constant domains are investigated. We begin by considering description logics with only one modal operator and then prove a general transfer theorem which makes it possible to lift the obtained results to many systems of polymodal description logic.