The main effort of the research in knowledge representation is providing theories and systems for expressing structured knowledge and for accessing and reasoning with it in a principled way. Description Logics are considered the most important knowledge representation formalism unifying and giving a logical basis to the well known traditions of Frame-based systems, Semantic Networks and KL-ONE-like languages, Object-Oriented representations, Semantic data models, and Type systems.
We study the problem of finite ontology mediated query answering (FOMQA), the variant of OMQA where the represented world is assumed to be finite, and thus only finite models of the ontology are considered. We adopt the most typical setting with unions of conjunctive queries and ontologies expressed in description logics (DLs). The study of FOMQA is relevant in settings that are not finitely controllable. This is the case not only for DLs without the finite model property, but also for those allowing transitive role declarations. When transitive roles are allowed, evaluating queries is challenging: FOMQA is undecidable for SHOIF and only known to be decidable for the Horn fragment of ALCIF. We show decidability of FOMQA for three proper fragments of SOIF: SOI, SOF, and SIF. Our approach is to characterise models relevant for deciding finite query entailment. Relying on a certain regularity of these models, we develop automata-based decision procedures with optimal complexity bounds.
We propose an algorithm for learning the Horn envelope of an arbitrary domain using an expert, or an oracle, capable of answering certain types of queries about this domain. Attribute exploration from formal concept analysis is a procedure that solves this problem, but the number of queries it may ask is exponential in the size of the resulting Horn formula in the worst case. We recall a well-known polynomial-time algorithm for learning Horn formulas with membership and equivalence queries and modify it to obtain a polynomial-time probably approximately correct algorithm for learning the Horn envelope of an arbitrary domain.
Schnattinger, Klemens (Baden-Wuerttemberg Cooperative State University Loerrach) | Mueller, Nadine (Baden-Wuerttemberg Cooperative State University Loerrach) | Walterscheid, Heike (Baden-Wuerttemberg Cooperative State University Loerrach)
The paper focuses on the applicability of a consensus mining model for group decision making. There seem to be no mechanism for translating different preferences of rational individuals or homogeneous preferences of groups into a coherent group preference that is not either itself irrational or dictatorial. Therefore, we are expanding the opinion mining architecture OMA, which brings opinions with weighted description logics into a ranking, to include incomplete fuzzy preference relations. In this work we will verify how feasible fuzzy modeling algorithms are in the German coalition negotiations in autumn 2017.
This article surveys previous work on combining planning techniques with expressive representations of knowledge in description logics to reason about tasks, plans, and goals. Description logics can reason about the logical definition of a class and automatically infer class-subclass subsumption relations as well as classify instances into classes based on their definitions. Descriptions of actions, plans, and goals can be exploited during plan generation, plan recognition, or plan evaluation. These techniques should be of interest to planning practitioners working on knowledge-rich application domains. Another emerging use of these techniques is the semantic web, where current ontology languages based on description logics need to be extended to reason about goals and capabilities for web services and agents.
Data integration is the problem of combining data residing at different autonomous, heterogeneous sources and providing the client with a unified, reconciled global view of the data. We discuss dataintegration systems, taking the abstract viewpoint that the global view is an ontology expressed in a class-based formalism. We resort to an expressive description logic, ALCQI, that fully captures classbased representation formalisms, and we show that query answering in data integration, as well as all other relevant reasoning tasks, is decidable. However, when we have to deal with large amounts of data, the high computational complexity in the size of the data makes the use of a fullfledged expressive description logic infeasible in practice. This leads us to consider DL-Lite, a specifically tailored restriction of ALCQI that ensures tractability of query answering in data integration while keeping enough expressive power to capture the most relevant features of class-based formalisms.
Information incompleteness, or ignorance, is an issue that we have to consider in Semantic Web applications. Dempster-Shafer theory has been traditionally applied in information incompleteness situations. On the other hand, logic plays a major role in the Semantic Web community. In this paper, we propose a framework that applies Dempster-Shafer theory in a Description Logic Knowledge Base environment. We name our model a Dempster-Shafer DL Knowledge Base.
Evolution of Knowledge Bases (KBs) consists of incorporating new information in an existing KB. Previous studies assume that the new information should be fully trusted and thus completely incorporated in the old knowledge. We suggest a setting where the new knowledge can be partially trusted and develop model-based approaches (MBAs) to KB evolution that rely on this assumption. Under MBAs the result of evolution is a set of interpretations and thus two core problems for MBAs are closure, i.e., whether evolution result can be axiomatised with a KB, and approximation, i.e., whether it can be (maximally) approximated with a KB. We show that DL-Lite is not closed under a wide range of trust-sensitive MBAs. We introduce a notion of s-approximation that improves the previously proposed approximations and show how to compute it for various trust-sensitive MBAs.
We study description logics (DLs) supporting number restrictions on transitive roles. We first take a look at SOQ and SON with binary and unary coding of numbers, and provide algorithms for the satisfiability problem and tight complexity bounds ranging from EXPTIME to NEXPTIME. We then show that by allowing for counting only up to one (functionality), inverse roles and role inclusions can be added without losing decidability. We finally investigate DLs of the DL-Lite-family, and show that, in the presence of role inclusions, the core fragment becomes undecidable.
Description logics are embodied in several knowledge-based systems and are used to develop various real-life applications. Now in paperback, The Description Logic Handbook provides a thorough account of the subject, covering all aspects of research in this field, namely: theory, implementation, and applications. Its appeal will be broad, ranging from more theoretically oriented readers, to those with more practically oriented interests who need a sound and modern understanding of knowledge representation systems based on description logics. As well as general revision throughout the book, this new edition presents a new chapter on ontology languages for the semantic web, an area of great importance for the future development of the web. In sum, the book will serve as a unique resource for the subject, and can also be used for self-study or as a reference for knowledge representation and artificial intelligence courses.
Enrico Franconi's Course on Description Logics The material includes slides for 6 modules ( 320 slides): A review of Computational Logics, Structural Description Logics, Propositional Description Logics, Description Logics and Knowledge Bases, Description Logics and Logics, Description Logics and Databases. A web pointer to an online modified version of CRACK, allowing for tracing satisfiability proofs with tableaux, is provided. Pointers to relevant online literature are provided, too. Enrico Franconi's Course on Description Logics The material includes slides for 6 modules ( 320 slides): A review of Computational Logics, Structural Description Logics, Propositional Description Logics, Description Logics and Knowledge Bases, Description Logics and Logics, Description Logics and Databases. A web pointer to an online modified version of CRACK, allowing for tracing satisfiability proofs with tableaux, is provided.