Standard and Non-standard reasoning in Description Logics

The present work deals with Description Logics (DLs), a class of knowledge representation formalisms used to represent and reason about classes of individuals and relations between such classes in a formally well-defined way. We provide novel results in three main directions. (1) Tractable reasoning revisited: in the 1990s, DL research has largely answered the question for practically relevant yet tractable DL formalisms in the negative. Due to novel application domains, especially the Life Sciences, and a surprising tractability result by Baader, we have re-visited this question, this time looking in a new direction: general terminologies (TBoxes) and extensions thereof defined over the DL EL and extensions thereof. As main positive result, we devise EL++(D)-CBoxes as a tractable DL formalism with optimal expressivity in the sense that every additional standard DL constructor, every extension of the TBox formalism, or every more powerful concrete domain, makes reasoning intractable. (2) Non-standard inferences for knowledge maintenance: non-standard inferences, such as matching, can support domain experts in maintaining DL knowledge bases in a structured and well-defined way. In order to extend their availability and promote their use, the present work extends the state of the art of non-standard inferences both w.r.t. theory and implementation. Our main results are implementations and performance evaluations of known matching algorithms for the DLs ALE and ALN, optimal non-deterministic polynomial time algorithms for matching under acyclic side conditions in ALN and sublanguages, and optimal algorithms for matching w.r.t. cyclic (and hybrid) EL-TBoxes. (3) Non-standard inferences over general concept inclusion (GCI) axioms: the utility of GCIs in modern DL knowledge bases and the relevance of non-standard inferences to knowledge maintenance naturally motivate the question for tractable DL formalism in which both can be provided. As main result, we propose hybrid EL-TBoxes as a solution to this hitherto open question

Investigation of the tradeoff between expressiveness and complexity in description logics with spatial operators

Le Logiche Descrittive sono una famiglia di formalismi molto espressivi per la rappresentazione della conoscenza. Questi formalismi sono stati investigati a fondo dalla comunit\ue0 scientifica, ma, nonostante questo grosso interesse, sono state definite poche Description Logics con operatori spaziali e tutte centrate sul Region Connection Calculus. Nella mia tesi considero tutti i pi\uf9 importanti formalismi di Qualitative Spatial Reasoning per mereologie, mereo-topologie e informazioni sulla direzione e studio alcune tecniche generali di ibridazione. Nella tesi presento un\u2019introduzione ai principali formalismi di Qualitative Spatial Reasoning e le principali famiglie di Description Logics. Nel mio lavoro, introduco anche le tecniche di ibridazione per estendere le Description Logics al ragionamento su conoscenza spaziale e presento il potere espressivo dei linguaggi ibridi ottenuti. Vengono presentati infine un risultato generale di para-decidibilit\ue0 per logiche descrittive estese da composition-based role axioms e l\u2019analisi del tradeoff tra espressivit\ue0 e propriet\ue0 computazionali delle logiche descrittive spaziali.Description Logics are a family of expressive Knowledge-Representation formalisms that have been deeply investigated. Nevertheless the few examples of DLs with spatial operators in the current literature are defined to include only the spatial reasoning capabilities corresponding to the Region Connection Calculus. In my thesis I consider all the most important Qualitative Spatial Reasoning formalisms for mereological, mereo-topological and directional information and investigate some general hybridization techniques. I will present a short overview of the main formalisms of Qualitative Spatial Reasoning and the principal families of DLs. I introduce the hybridization techniques to extend DLs to QSR and present the expressiveness of the resulting hybrid languages. I also present a general paradecidability result for undecidable languages equipped with composition-based role axioms and the tradeoff analysis of expressiveness and computational properties for the spatial DLs

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.

Enumerating Query Plans via Conditional Tableau Interpolation

Database query optimization studies the problem of finding equivalent and efficient query execution plans for user queries under schema constraints. Logic-based approaches to query optimization leverage automated theorem proving and Craig interpolation to enumerate query plans that are correct and performance-optimal. In this thesis, we investigate and improve one of the state-of-the-art logic-based query optimizers – the Interpolation Test Bed (ITB). We begin by formally capturing the physical data independence framework and query optimization problem with first-order logic. Then, we give a gentle introduction to the classical results from logic that form the basis of logic-based query optimizers. We re-establish the correctness of ITB’s conditional tableau interpolation mechanism by reduction to free-variable tableau interpolation. To facilitate the reduction proof, we introduce interpolation rules for the free-variable tableau and prove the correctness of interpolation. Then we show the correctness of conditional tableau interpolation by reduction. We investigate a limitation of ITB’s forward chaining design, which causes missing optimal plans. To address this limitation, we propose a rewriting procedure inspired by Magic Set Transformation (MST), to extend the plan space for the current ITB system. We show that the propose rewriting procedure effectively generates the missing query plans, which are otherwise not found, while accommodating the existing forward chaining design

Scalable Reasoning for Knowledge Bases Subject to Changes

ScienceWeb is a semantic web system that collects information about a research community and allows users to ask qualitative and quantitative questions related to that information using a reasoning engine. The more complete the knowledge base is, the more helpful answers the system will provide. As the size of knowledge base increases, scalability becomes a challenge for the reasoning system. As users make changes to the knowledge base and/or new information is collected, providing fast enough response time (ranging from seconds to a few minutes) is one of the core challenges for the reasoning system. There are two basic inference methods commonly used in first order logic: forward chaining and backward chaining. As a general rule, forward chaining is a good method for a static knowledge base and backward chaining is good for the more dynamic cases. The goal of this thesis was to design a hybrid reasoning architecture and develop a scalable reasoning system whose efficiency is able to meet the interaction requirements in a ScienceWeb system when facing a large and evolving knowledge base. Interposing a backward chaining reasoner between an evolving knowledge base and a query manager with support of trust yields an architecture that can support reasoning in the face of frequent changes. An optimized query-answering algorithm, an optimized backward chaining algorithm and a trust-based hybrid reasoning algorithm are three key algorithms in such an architecture. Collectively, these three algorithms are significant contributions to the field of backward chaining reasoners over ontologies. I explored the idea of trust in the trust-based hybrid reasoning algorithm, where each change to the knowledge base is analyzed as to what subset of the knowledge base is impacted by the change and could therefore contribute to incorrect inferences. I adopted greedy ordering and deferring joins in optimized query-answering algorithm. I introduced four optimizations in the algorithm for backward chaining. These optimizations are: 1) the implementation of the selection function, 2) the upgraded substitute function, 3) the application of OLDT and 4) solving of the owl: sameAs problem. I evaluated our optimization techniques by comparing the results with and without optimization techniques. I evaluated our optimized query answering algorithm by comparing to a traditional backward-chaining reasoner. I evaluated our trust-based hybrid reasoning algorithm by comparing the performance of a forward chaining algorithm to that of a pure backward chaining algorithm. The evaluation results have shown that the hybrid reasoning architecture with the scalable reasoning system is able to support scalable reasoning of ScienceWeb to answer qualitative questions effectively when facing both a fixed knowledge base and an evolving knowledge base

A Framework for the Organization and Discovery of Information Resources in a WWW Environment Using Association, Classification and Deduction

The Semantic Web is envisioned as a next-generation WWW environment in which information is given well-defined meaning. Although the standards for the Semantic Web are being established, it is as yet unclear how the Semantic Web will allow information resources to be effectively organized and discovered in an automated fashion. This dissertation research explores the organization and discovery of resources for the Semantic Web. It assumes that resources on the Semantic Web will be retrieved based on metadata and ontologies that will provide an effective basis for automated deduction. An integrated deduction system based on the Resource Description Framework (RDF), the DARPA Agent Markup Language (DAML) and description logic (DL) was built. A case study was conducted to study the system effectiveness in retrieving resources in a large Web resource collection. The results showed that deduction has an overall positive impact on the retrieval of the collection over the defined queries. The greatest positive impact occurred when precision was perfect with no decrease in recall. The sensitivity analysis was conducted over properties of resources, subject categories, query expressions and relevance judgment in observing their relationships with the retrieval performance. The results highlight both the potentials and various issues in applying deduction over metadata and ontologies. Further investigation will be required for additional improvement. The factors that can contribute to degraded performance were identified and addressed. Some guidelines were developed based on the lessons learned from the case study for the development of Semantic Web data and systems