The Complexity of Satisfiability for Sub-Boolean Fragments of ALC

The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC, notably logics in the FL, EL, and DL-Lite family, have an easier satisfiability problem; sometimes it is even tractable. All these fragments restrict the use of Boolean operators in one way or another. We look at systematic and more general restrictions of the Boolean operators and establish the complexity of the concept satisfiability problem in the presence of axioms. We separate tractable from intractable cases.Comment: 17 pages, accepted (in short version) to Description Logic Workshop 201

Adding weight to DL-Lite

In this paper we extend the logic DL-LiteNbool and its fragments with (i) role inclusions, (ii) qualified number restrictions and (iii) role disjointness, symmetry, asymmetry, reflexivity and irreflexivity constraints. We show that if the interaction of (qualified) number restrictions with role inclusions is restricted in a way similar to DL-LiteA then the resulting logics enjoy the same computational properties as the respective fragments of DL-LiteNbool: for combined complexity, satisfiability in the full language is NP-complete and it is tractable in the Horn fragment; for data complexity, answering positive existential queries over the Horn fragment is in AC0 (and thus, FO rewritable). Our main tool for dealing with DL-Lite logics is embedding into the one-variable fragment of first-order logic without equality and function symbols, which seems to be a natural logic-based characterization of the DL-Lite logics. This embedding provides us with upper combined complexity bounds for all fragments. We also use it to obtains explicit FO rewritings of positive existential queries for the Horn fragment