Adding Threshold Concepts to the Description Logic EL

We introduce an extension of the lightweight Description Logic EL that allows us to de_ne concepts in an approximate way. For this purpose, we use a graded membership function, which for each individual and concept yields a number in the interval [0, 1] expressing the degree to which the individual belongs to the concept. Threshold concepts C~t for ~ then collect all the individuals that belong to C with degree ~ t. We generalize a well-known characterization of membership in EL concepts to construct a specific graded membership function deg, and investigate the complexity of reasoning in the Description Logic τEL(deg), which extends EL by threshold concepts defined using deg. We also compare the instance problem for threshold concepts of the form C>t in τEL(deg) with the relaxed instance queries of Ecke et al

05171 Abstracts Collection -- Nonmonotonic Reasoning, Answer Set Programming and Constraints

From 24.04.05 to 29.04.05, the Dagstuhl Seminar 05171 ``Nonmonotonic Reasoning, Answer Set Programming and Constraints\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Implementing Preferences with asprin

asprin offers a framework for expressing and evaluating combinations of quantitative and qualitative preferences among the stable models of a logic program. In this paper, we demonstrate the generality and flexibility of the methodology by showing how easily existing preference relations can be implemented in asprin. Moreover, we show how the computation of optimal stable models can be improved by using declarative heuristics. We empirically evaluate our contributions and contrast them with dedicated implementations. Finally, we detail key aspects of asprin’s implementation.Full Tex

Generalizations of dung frameworks and their role in formal argumentation

This article provides a short survey of some of the most popular abstract argumentation frameworks available today. The authors present the general idea of abstract argumentation, highlighting the role of abstract frameworks in the argumentation process, and review the original Dung frameworks and their semantics. A discussion of generalizations of these frameworks follows, focusing on structures taking preferences and values into account and approaches in which not only attack but also support relations can be modeled. Finally, the authors review the concept of abstract dialectical frameworks, one of the most general systems for abstract argumentation providing a flexible, principled representation of arbitrary argument relations

Inconsistency Management in Reactive Multi-context Systems

FCT grant SFRH/BPD/100906/2014 and M. Knorr by FCT grant SFRH/BPD/86970/2012. German Research Foundation (DFG) grants BR-1817/7-1 and FOR 1513We address the problem of global inconsistency in reactive multi-context systems (rMCSs), a framework for reactive reasoning in the presence of heterogeneous knowledge sources that can deal with continuous input streams. Their semantics is given in terms of equilibria streams. The occurrence of inconsistencies, where rMCSs fail to have an equilibria stream, can render the entire system useless. We discuss various methods for handling this problem, following different strategies such as repairing the rMCS, or even relaxing the notion of equilibria stream so that it can go through inconsistent states.proofpublishe

Heterogeneous reasoning in dynamic environments

We would like to thank K. Schekotihin and the anonymous reviewers for their comments, which helped improving this paper. G. Brewka, S. Ellmauthaler, and J. Puhrer were partially supported by the German Research Foundation (DFG) under grants BR-1817/7-1/2 and FOR 1513. R. Goncalves, M. Knorr and J. Leite were partially supported by Fundacao para a Ciencia e a Tecnologia (FCT) under project NOVA LINCS (UID/CEC/04516/2013). Moreover, R. Goncalves was partially supported by FCT grant SFRH/BPD/100906/2014 and M. Knorr by FCT grant SFRH/BPD/86970/2012.Managed multi-context systems (mMCSs) allow for the integration of heterogeneous knowledge sources in a modular and very general way. They were, however, mainly designed for static scenarios and are therefore not well-suited for dynamic environments in which continuous reasoning over such heterogeneous knowledge with constantly arriving streams of data is necessary. In this paper, we introduce reactive multi-context systems (rMCSs), a framework for reactive reasoning in the presence of heterogeneous knowledge sources and data streams. We show that rMCSs are indeed well-suited for this purpose by illustrating how several typical problems arising in the context of stream reasoning can be handled using them, by showing how inconsistencies possibly occurring in the integration of multiple knowledge sources can be handled, and by arguing that the potential non-determinism of rMCSs can be avoided if needed using an alternative, more skeptical well-founded semantics instead with beneficial computational properties. We also investigate the computational complexity of various reasoning problems related to rMCSs. Finally, we discuss related work, and show that rMCSs do not only generalize mMCSs to dynamic settings, but also capture/extend relevant approaches w.r.t. dynamics in knowledge representation and stream reasoning.publishe