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.
Description logics are knowledge representation languages that have been designed to strike a balance between expressivity and computational tractability. Many different description logics have been developed, and numerous computational problems for these logics have been studied for their computational complexity. However, essentially all complexity analyses of reasoning problems for description logics use the one-dimensional framework of classical complexity theory. The multi-dimensional framework of parameterized complexity theory is able to provide a much more detailed image of the complexity of reasoning problems. In this paper we argue that the framework of parameterized complexity has a lot to offer for the complexity analysis of description logic reasoning problems---when one takes a progressive and forward-looking view on parameterized complexity tools. We substantiate our argument by means of three case studies. The first case study is about the problem of concept satisfiability for the logic ALC with respect to nearly acyclic TBoxes. The second case study concerns concept satisfiability for ALC concepts parameterized by the number of occurrences of union operators and the number of occurrences of full existential quantification. The third case study offers a critical look at data complexity results from a parameterized complexity point of view. These three case studies are representative for the wide range of uses for parameterized complexity methods for description logic problems.
We study the problem of finite ontology mediated query an-swering (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 isrelevant 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.
Baader, Franz (Technische Universität Dresden ) | Kriegel, Francesco (Technische Universität Dresden) | Nuradiansyah, Adrian (Technische Universität Dresden) | Peñaloza, Rafael (Free University of Bozen-Bolzano)
The classical approach for repairing a Description Logic ontology O in the sense of removing an unwanted consequence c is to delete a minimal number of axioms from O such that the resulting ontology O' does not have the consequence c. However, the complete deletion of axioms may be too rough, in the sense that it may also remove consequences that are actually wanted. To alleviate this problem, we propose a more gentle notion of repair in which axioms are not deleted, but only weakened. On the one hand, we investigate general properties of this gentle repair method. On the other hand, we propose and analyze concrete approaches for weakening axioms expressed in the Description Logic EL.
Standard reasoning problems are complete for EXPTIME in common feature-based description logics-ones in which all roles are restricted to being functional. We show how to control conjunctions on left-hand-sides of subsumptions in such a way so as to ensure polynomial time complexity. In particular, we present a PTIME algorithm for reasoning about knowledge base consistency. We then show how the resulting description logic allows features to be partial, not just total functions. Algorithms for polynomial-time query answering are presented. The above, in combination with referring expressions, provide a richer capability for ontology-based data access to relational data sources.
In this extended abstract we discuss the relationship between confidentiality-preserving frameworks and inconsistency-tolerant repair and update semantics in Description Logics (DL). In particular, we consider the wellknown problems of Consistent Query Answering, Controlled Query Evaluation, and Knowledge Base Update in DL and introduce a unifying framework that can be naturally instantiated to capture significant settings for the above problems, previously investigated in the literature. It is a declarative approach to manage inconsistency that has been extensively studied in both databases and knowledge bases (KBs) (Bertossi 2011; Bienvenu and Bourgaux 2016). The crucial notions for CQA are those of repair and consistent answers. Several notions of minimality can be adopted, which in general give rise to the existence of several repairs.
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.