We define the notion of rational closure in the context of Description Logics extended with a tipicality operator. We start from ALC+T, an extension of ALC with a typicality operator T: intuitively allowing to express concepts of the form T(C), meant to select the "most normal" instances of a concept C. The semantics we consider is based on rational model. But we further restrict the semantics to minimal models, that is to say, to models that minimise the rank of domain elements. We show that this semantics captures exactly a notion of rational closure which is a natural extension to Description Logics of Lehmann and Magidor's original one. We also extend the notion of rational closure to the Abox component. We provide an ExpTime algorithm for computing the rational closure of an Abox and we show that it is sound and complete with respect to the minimal model semantics.

Description logic Knowledge and Action Bases (KAB) are a mechanism for providing both a semantically rich representation of the information on the domain of interest in terms of a description logic knowledge base and actions to change such information over time, possibly introducing new objects. We resort to a variant of DL-Lite where the unique name assumption is not enforced and where equality between objects may be asserted and inferred. Actions are specified as sets of conditional effects, where conditions are based on epistemic queries over the knowledge base (TBox and ABox), and effects are expressed in terms of new ABoxes. In this setting, we address verification of temporal properties expressed in a variant of first-order mu-calculus with quantification across states. Notably, we show decidability of verification, under a suitable restriction inspired by the notion of weak acyclicity in data exchange.

This paper describes the analysis of a selected testbed of Semantic Web ontologies, by a SPARQL query, which determines those ontologies that can be related to the description logic DL, introduced in [4] and studied in [9]. We will see that a reasonable number of them is expressible within such computationally efficient language. We expect that, in a long-term view, a temporalization of description logics, and consequently, of OWL(2), can open new perspectives for the inclusion in this language of a greater number of ontologies of the testbed and, hopefully, of the "real world".

A major challenge of pervasive context-aware computing and intelligent environments resides in the acquisition and modelling of rich and heterogeneous context data. Decisive aspects of this information are the ongoing human activities at different degrees of granularity. We conjecture that ontology-based activity models are key to support interoperable multilevel activity representation and recognition. In this paper, we report on an initial investigation about the application of probabilistic description logics (DLs) to a framework for the recognition of multilevel activities in intelligent environments. In particular, being based on Log-linear DLs, our approach leverages the potential of highly expressive description logics with probabilistic reasoning in one unified framework. While we believe that this approach is very promising, our preliminary investigation suggests that challenging research issues remain open, including extensive support for temporal reasoning, and optimizations to reduce the computational cost.

We tackle the problem of defining a well-founded semantics for Datalog rules with existentially quantified variables in their heads and negations in their bodies. In particular, we provide a well-founded semantics (WFS) for the recent Datalog+/- family of ontology languages, which covers several important description logics (DLs). To do so, we generalize Datalog+/- by non-stratified nonmonotonic negation in rule bodies, and we define a WFS for this generalization via guarded fixed-point logic. We refer to this approach as equality-friendly WFS, since it has the advantage that it does not make the unique name assumption (UNA); this brings it close to OWL and its profiles as well as typical DLs, which also do not make the UNA. We prove that for guarded Datalog+/- with negation under the equality-friendly WFS, conjunctive query answering is decidable, and we provide precise complexity results for this problem. From these results, we obtain precise definitions of the standard WFS extensions of EL and of members of the DL-Lite family, as well as corresponding complexity results for query answering.

This paper presents complexity analysis and variational methods for inference in probabilistic description logics featuring Boolean operators, quantification, qualified number restrictions, nominals, inverse roles and role hierarchies. Inference is shown to be PEXP-complete, and variational methods are designed so as to exploit logical inference whenever possible.

We propose a novel, type-elimination-based method for reasoning in the description logic SHIQbs including DL-safe rules. To this end, we first establish a knowledge compilation method converting the terminological part of an ALCIb knowledge base into an ordered binary decision diagram (OBDD) which represents a canonical model. This OBDD can in turn be transformed into disjunctive Datalog and merged with the assertional part of the knowledge base in order to perform combined reasoning. In order to leverage our technique for full SHIQbs, we provide a stepwise reduction from SHIQbs to ALCIb that preserves satisfiability and entailment of positive and negative ground facts. The proposed technique is shown to be worst case optimal w.r.t. combined and data complexity and easily admits extensions with ground conjunctive queries.

In this paper, we study the problem of exchanging knowledge between a source and a target knowledge base (KB), connected through mappings. Differently from the traditional database exchange setting, which considers only the exchange of data, we are interested in exchanging implicit knowledge. As representation formalism we use Description Logics (DLs), thus assuming that the source and target KBs are given as a DL TBox+ABox, while the mappings have the form of DL TBox assertions. We study the problem of translating the knowledge in the source KB according to these mappings. We define a general framework of KB exchange, and address the problems of representing implicit source information in the target, and of computing different kinds of solutions, i.e., target KBs with specified properties, given a source KB and a mapping. We develop first results and study the complexity of KB exchange for DL-Lite_RDFS, a DL corresponding to the FOL fragment of RDFS, and for DL-Lite_R.

We study (i) uniform interpolation for TBoxes that are formulated in the description logic EL and (ii) approximations of TBoxes formulated in more expressive languages. In both cases, we give model-theoretic characterizations based on simulations and cartesian products, and we develop algorithms that decide whether interpolants and approximations exist. We present a uniform approach to both problems, based on a novel amorphous automaton model called EL automata (EA). Using EAs, we also establish a simpler proof of the known result that conservative extensions of EL-TBoxes can be decided in ExpTime.

Fuzzy description logics (DLs) have been investigated for over two decades, due to their capacity to formalize and reason with imprecise concepts. Very recently, it has been shown that for several fuzzy DLs, reasoning becomes undecidable. Although the proofs of these results differ in the details of each specific logic considered, they are all based on the same basic idea. In this paper, we formalize this idea and provide sufficient conditions for proving undecidability of a fuzzy DL. We demonstrate the effectiveness of our approach by strengthening all previously-known undecidability results and providing new ones. In particular, we show that undecidability may arise even if only crisp axioms are considered.