Abstract. The DL-Lite family of tractable description logics lies between the semantic web languages RDFS and OWL Lite. In this paper, we present a probabilistic generalization of the DL-Lite description logics, which is based on Bayesian networks. As an important feature, the new probabilistic description logics allow for flexibly combining terminological and assertional pieces of probabilistic knowledge. We show that the new probabilistic description logics are rich enough to properly extend both the DL-Lite description logics as well as Bayesian networks. We also show that satisfiability checking and query processing in the new probabilistic description logics is reducible to satisfiability checking and query processing in the DL-Lite family. Furthermore, we show that satisfiability checking and answering unions of conjunctive queries in the new logics can be done in LogSpace in the data complexity. For this reason, the new probabilistic description logics are very promising formalisms for data-intensive applications in the Semantic Web involving probabilistic uncertainty. Key words: Bayesian description logics, tractable reasoning, description logics,

In this paper, we leverage annotated logic programs for tracking indicators of provenance and trust during reasoning, specifically focussing on the use-case of applying a scalable subset of OWL 2 RL/RDF rules over static corpora of arbitrary Linked Data (Web data). Our annotations encode three facets of information: (i) blacklist: a (possibly manually generated) boolean annotation which indicates that the referent data are known to be harmful and should be ignored during reasoning; (ii) ranking: a numeric value derived by a PageRank-inspired technique—adapted for Linked Data—which determines the centrality of certain data artefacts (such as RDF documents and statements); (iii) authority: a boolean value which uses Linked Data principles to conservatively determine whether or not some terminological information can be trusted. We formalise a logical framework which annotates inferences with the strength of derivation along these dimensions of trust and provenance; we formally demonstrate some desirable properties of the deployment of annotated logic programming in our setting, which guarantees (i) a unique minimal model (least fixpoint); (ii) monotonicity; (iii) finitariness; and (iv) finally decidability. In so doing, we also give some formal results which reveal strategies for scalable and efficient implementation of various reasoning tasks one might consider. Thereafter, we discuss scalable and distributed implementation strategies for applying our ranking and reasoning methods over a cluster of commodity hardware; throughout, we provide evaluation of our methods over 1 billion Linked Data quadruples crawled from approximately 4 million individual Web documents, empirically demonstrating the scalability of our approach, and how our

Abstract. A usage scenario of bio-ontologies is hypothesis testing, such as finding relationships or new subconcepts in the data linked to the ontology. Whilst validating the hypothesis, such knowledge is uncertain or vague and the data is often incomplete, which DL knowledge bases do not take into account. In addition, it requires scalability with large amounts of data. To address these requirements, we take the SROIQ(D) and DL-Lite family of languages and their application infrastructures augmented with notions of rough sets. Although one can represent only little of rough concepts in DL-Lite, useful aspects can be dealt with in the mapping layer that links the concepts in the ontology to queries over the data source. We discuss the trade-offs and demonstrate validation of the theoretical assessment with the HGT application ontology about horizontal gene transfer and its 17GB database by taking advantage of the Ontology-Based Data Access framework. However, the prospects for comprehensive and usable rough DL knowledge bases are not good, and may require both sophisticated modularization and scientific workflows to achieve systematic use of rough ontologies. 1

During the recent decade, handling uncertainty has started to play an important role in ontology languages, especially in application areas like the Semantic Web, Bio-medicine, and Artificial Intelligence. For this reason, there is currently a strong research interest in Description Logics (DLs) that allow for dealing

Fuzzy Description Logics are a family of logics which allow to deal with structured knowledge affected by vagueness. Although a relatively important amount of work has been carried out in the last years, current fuzzy DLs are open to be extend with several features worked out in the fuzzy logic literature. In this work, we extend fuzzy DLs with fuzzy truth values, allowing to state sentences such as “Tina is young is almost true”.

Abstract. Exceptions play an important role in conceptualizing data, especially when new knowledge is introduced or existing knowledge changes. Furthermore, real-world data often is contradictory and uncertain. Current formalisms for conceptualizing data like Description Logics rely upon first-order logic. As a consequence, they are poor in addressing exceptional, inconsistent and uncertain data, in particular when evolving the knowledge base over time. This paper investigates the use of Probabilistic Description Logics as a formalism for the evolution of ontologies that conceptualize real-world data. Different scenarios are presented for the automatic handling of inconsistencies during ontology evolution. The year is 50 B.C. Gaul is entirely occupied by the Romans. Well, not entirely... One small village of indomitable Gauls still holds out against the invadors. And life is not easy for the Roman legionaries who garrison the fortified

Fuzzy Description Logics (DLs) are a family of logics which allow the representation of (and the reasoning within) structured knowledge affected by vagueness. Although a relatively important amount of work has been carried out in the last years, little attention has been given to the role of datatypes in fuzzy DLs. This paper presents a fuzzy DL with three kinds of extended datatype restrictions, together with the necessary rules to reason with them.

The problem of grasping is widely studied in the robotics community. This project focuses on the identification of object graspable features using images and object structural information. The primary aim is the creation of a framework in which the information gathered by the vision system can be integrated with automatically generated knowledge, modelled by means of fuzzy description logics. 1

Uncertainty is unavoidable when modeling most application domains. In medicine, for example, symptoms (such as pain, dizziness, or nausea) are always subjective, and hence imprecise and incomparable. Additionally, concepts and their relationships may be inexpressible in a crisp, clear-cut manner. We extend the description logic ALC with multi-valued semantics based on lattices that can handle uncertainty on concepts as well as on the axioms of the ontology. We introduce reasoning methods for this logic w.r.t. general concept inclusions and show that the complexity of reasoning is not increased by this new semantics. 1

Uncertainty and vagueness are pervasive phenomena in real-life knowledge. They are supported in extended description logics that adapt classical description logics to deal with numerical probabilities or fuzzy truth degrees. While the two concepts are distinguished for good reasons, they combine in the notion of probably, which is ultimately a fuzzy qualification of probabilities. Here, we develop existing propositional logics of fuzzy probability into a full-blown description logic, and we show decidability of several variants of this logic under Łukasiewicz semantics. We obtain these results in a novel generic framework of fuzzy coalgebraic logic; this enables us to extend our results to logics that combine crisp ingredients including standard crisp roles and crisp numerical probabilities with fuzzy roles and fuzzy probabilities. 1