On the Computation of Common Subsumers in Description Logics

Description logics (DL) knowledge bases are often build by users with expertise in the application domain, but little expertise in logic. To support this kind of users when building their knowledge bases a number of extension methods have been proposed to provide the user with concept descriptions as a starting point for new concept definitions. The inference service central to several of these approaches is the computation of (least) common subsumers of concept descriptions. In case disjunction of concepts can be expressed in the DL under consideration, the least common subsumer (lcs) is just the disjunction of the input concepts. Such a trivial lcs is of little use as a starting point for a new concept definition to be edited by the user. To address this problem we propose two approaches to obtain "meaningful" common subsumers in the presence of disjunction tailored to two different methods to extend DL knowledge bases. More precisely, we devise computation methods for the approximation-based approach and the customization of DL knowledge bases, extend these methods to DLs with number restrictions and discuss their efficient implementation

Completion-based computation of most specific concepts with limited role-depth for EL and Prob-EL⁰¹

In Description Logics the reasoning service most specific concept (msc) constructs a concept description that generalizes an ABox individual into a concept description. For the Description Logic EL the msc may not exist, if computed with respect to general EL-TBoxes or cyclic ABoxes. However, it is still possible to find a concept description that is the msc up to a fixed role-depth, i.e. with respect to a maximal nesting of quantifiers. In this report we present a practical approach for computing the roledepth bounded msc, based on the polynomial-time completion algorithm for EL. We extend these methods to Prob-EL⁰¹c , which is a probabilistic variant of EL. Together with the companion report [9] this report devises computation methods for the bottom-up construction of knowledge bases for EL and Prob-EL⁰¹c

Tractable approximate deduction for OWL

Acknowledgements This work has been partially supported by the European project Marrying Ontologies and Software Technologies (EU ICT2008-216691), the European project Knowledge Driven Data Exploitation (EU FP7/IAPP2011-286348), the UK EPSRC project WhatIf (EP/J014354/1). The authors thank Prof. Ian Horrocks and Dr. Giorgos Stoilos for their helpful discussion on role subsumptions. The authors thank Rafael S. Gonçalves et al. for providing their hotspots ontologies. The authors also thank BoC-group for providing their ADOxx Metamodelling ontologies.Peer reviewedPostprin

Approximating FOL Ontologies using OWL2

With the amount of data collected everyday ever expanding, techniques which allow com- puters to semantically understand data are growing in importance. Ontologies are a tool to describe the relationships connecting data so that computers can correctly interpret and combine data from many sources. An ontology about water needs to describe what the term river may refer to: An arbitrary river or one usable for navigation; a single tributary or an entire river network; the riverbed or the water itself? Well-designed ontologies can be shared, reused, and extended across multiple applications and facilitate betters integration of different data collections. Common Logic (CL) and the Web Ontology Language (OWL) are two logic based languages of popular interest. However, ontologies developed in either of these languages are not easily consumed by users of the other language. By utilizing the first order properties of Common Logic, an automated approximation routine between CL and OWL is provided. OWL, being less expressive than CL, is capable of being totally represented by logically equivalent CL axioms. Leveraging the logical equivalence, we provide a method of axiom normalization and extraction in order to construct robust OWL ontologies from existing CL sources. This increases CL ontology intelligibility, and allows the automatic construction of OWL versions of existing reference ontologies. Further, the benefits of such a translation are demonstrated by applying previously exclusive OWL tooling and analysis techniques to evaluate the translated ontologies

Approximate Assertional Reasoning Over Expressive Ontologies

In this thesis, approximate reasoning methods for scalable assertional reasoning are provided whose computational properties can be established in a well-understood way, namely in terms of soundness and completeness, and whose quality can be analyzed in terms of statistical measurements, namely recall and precision. The basic idea of these approximate reasoning methods is to speed up reasoning by trading off the quality of reasoning results against increased speed

Uniform Interpolation and Forgetting for ALC Ontologies with ABoxes

Uniform interpolation and the dual task of forgetting restrict the ontology to a specified subset of concept and role names. This makes them useful tools for ontology analysis, ontology evolution and information hiding. Most previous research focused on uniform interpolation of TBoxes. However, especially for applications in privacy and information hiding, it is essential that uniform interpolation methods can deal with ABoxes as well. We present the first method that can compute uniform interpolants of any ALC ontology with ABoxes. ABoxes bring their own challenges when computing uniform interpolants, possibly requiring disjunctive statements or nominals in the resulting ABox. Our method can compute representations of uniform interpolants in ALCO. An evaluation on realistic ontologies shows that these uniform interpolants can be practically computed, and can often even be presented in pure ALC

Subset reasoning for event-based systems

In highly dynamic domains such as the Internet of Things (IoT), smart industries, smart manufacturing, pervasive health or social media, data is being continuously generated. By combining this generated data with background knowledge and performing expressive reasoning upon this combination, meaningful decisions can be made. Furthermore, this continuously generated data typically originates from multiple heterogeneous sources. Ontologies are ideal for modeling the domain and facilitates the integration of heterogeneous produced data with background knowledge. Furthermore, expressive ontology reasoning allows to infer implicit facts and enables intelligent decision making. The data produced in these domains is often volatile. Time-critical systems, such as IoT Nurse Call systems, require timely processing of the produced IoT data. However, there is still a mismatch between volatile data and expressive ontology reasoning, since the incoming data frequency is often higher than the reasoning time. For this reason, we present an approximation technique that allows to extract a subset of data to speed-up the reasoning process. We demonstrate this technique in a Nurse Call proof of concept where the locations of the nurses are tracked and the most suited nurse is selected when the patient launches a call and in an extension of an existing benchmark. We managed to speed up the reasoning process up to 10 times for small datasets and up to more than 1000 times for large datasets