Reasoning Algebraically with Description Logics

Semantic Web applications based on the Web Ontology Language (OWL) often require the use of numbers in class descriptions for expressing cardinality restrictions on properties or even classes. Some of these cardinalities are specified explicitly, but quite a few are entailed and need to be discovered by reasoning procedures. Due to the Description Logic (DL) foundation of OWL, those reasoning services are offered by DL reasoners. Existing DL reasoners employ reasoning procedures that are arithmetically uninformed and substitute arithmetic reasoning by "don't know" non-determinism in order to cover all possible cases. This lack of information about arithmetic problems dramatically degrades the performance of DL reasoners in many cases, especially with ontologies relying on the use of Nominals and Qualied Cardinality Restrictions. The contribution of this thesis is twofold: on the theoretical level, it presents algebra�ic reasoning with DL (ReAl DL) using a sound, complete, and terminating reasoning procedure for the DL SHOQ. ReAl DL combines tableau reasoning procedures with algebraic methods, namely Integer Programming, to ensure arithmetically better informed reasoning. SHOQ extends the standard DL ALC with transitive roles, role hierarchies, qualified cardinality restrictions (QCRs), and nominals, and forms an expressive subset of OWL. Although the proposed algebraic tableau is double exponential in the worst case, it deals with cardinalities with an additional level of information and properties that make the calculus amenable and well suited for optimizations. In order for ReAl DL to have a practical merit, suited optimizations are proposed towards achieving an efficient reasoning approach that addresses the sources of complexity related to nominals and QCRs. On the practical level, a running prototype reasoner (HARD) is implemented based on the proposed calculus and optimizations. HARD is used to evaluate the practical merit of ReAl DL, as well as the effectiveness of the proposed optimizations. Experimental results based on real world and synthetic ontologies show that ReAl DL outperforms existing reasoning approaches in handling the interactions between nominals and QCRs. ReAl DL also comes with some interesting features such as the ability to handle ontologies with cyclic descriptions without adopting special blocking strategies. ReAl DL can form a basis to provide more efficient reasoning support for ontologies using nominals or QCRs

Modelování n-árních relací v deskripčních logikách

DLR is an expressive description logic with support of n-ary relations. Currently, there is no known algorithm for native reasoning within DLR. However there are two approaches that allow to delegate reasoning services of DLR to binary description logics. In this work we de ne new description logic NDL, a subset of DLR, for which we believe that native reasoning can be provided. Based on the existing approaches, we transform NDL to binary description logics for which the current of state-of-art of reasoners exist. New transformations will be analysed both theoretically and empirically. N-ary data for benchmark will be created from existing OWL ontologies by transformation of opposite direction. This benchmark can be used for comparison of native reasoning and reasoning by transformation to binary DLs.DLR je expresívna deskripčná logika, ktorá podporuje n-árne relácie. V súčastnosti neexistuje algoritmus, ktorý by dokázal natívne uvažovať v DLR. Existujú však dve práce, ktoré umožňujú uvažovanie delegovať do binárnych logík. V tejto práci de finujeme novú deskripčnú logiku NDL. Tá predstavuje podmnožinu DLR, pre ktorú veríme, že natívne uvažovanie vieme poskytnúť. Na základe spomínaných prací vytvoríme transformácie z NDL do binárnych logík, ktoré budeme mocť použiť v najmodernejších odvodzovacích systémoch. Nové transformácie teoreticky i prakticky analyzujeme. N-árne data pre testovanie vytvoríme z existujúcich OWL ontológií opačnou transformáciou. Táto práca môže byť použita pre porovnanie natívneho uvažovania a uvažovania pomocou transformácie do binárnych logík.Department of Software EngineeringKatedra softwarového inženýrstvíMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

OPTIMIZATION OF NONSTANDARD REASONING SERVICES

The increasing adoption of semantic technologies and the corresponding increasing complexity of application requirements are motivating extensions to the standard reasoning paradigms and services supported by such technologies. This thesis focuses on two of such extensions: nonmonotonic reasoning and inference-proof access control. Expressing knowledge via general rules that admit exceptions is an approach that has been commonly adopted for centuries in areas such as law and science, and more recently in object-oriented programming and computer security. The experiences in developing complex biomedical knowledge bases reported in the literature show that a direct support to defeasible properties and exceptions would be of great help. On the other hand, there is ample evidence of the need for knowledge confidentiality measures. Ontology languages and Linked Open Data are increasingly being used to encode the private knowledge of companies and public organizations. Semantic Web techniques facilitate merging different sources of knowledge and extract implicit information, thereby putting at risk security and the privacy of individuals. But the same reasoning capabilities can be exploited to protect the confidentiality of knowledge. Both nonmonotonic inference and secure knowledge base access rely on nonstandard reasoning procedures. The design and realization of these algorithms in a scalable way (appropriate to the ever-increasing size of ontologies and knowledge bases) is carried out by means of a diversified range of optimization techniques such as appropriate module extraction and incremental reasoning. Extensive experimental evaluation shows the efficiency of the developed optimization techniques: (i) for the first time performance compatible with real-time reasoning is obtained for large nonmonotonic ontologies, while (ii) the secure ontology access control proves to be already compatible with practical use in the e-health application scenario.