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## Über dieses Buch

This book contains revised and significantly extended versions of selected papers from three workshops on Uncertainty Reasoning for the Semantic Web (URSW), held at the International Semantic Web Conferences (ISWC) in 2008, 2009, and 2010 or presented at the first international Workshop on Uncertainty in Description Logics (UniDL), held at the Federated Logic Conference (FLoC) in 2010. The 17 papers presented were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on probabilistic and Dempster-Shafer models, fuzzy and possibilistic models, inductive reasoning and machine learning, and hybrid approaches.

## Inhaltsverzeichnis

### PR-OWL 2.0 – Bridging the Gap to OWL Semantics

Abstract
The past few years have witnessed an increasingly mature body of research on the Semantic Web (SW), with new standards being developed and more complex use cases being proposed and explored. As complexity increases in SW applications, so does the need for principled means to represent and reason with uncertainty in SW applications. One candidate representation for uncertainty representation is PR-OWL, which provides OWL constructs for representing Multi-Entity Bayesian Network (MEBN) theories. This paper reviews some shortcomings of PR-OWL 1.0 and describes how they are addressed in PR-OWL 2. A method is presented for mapping back and forth between OWL properties and MEBN random variables (RV). The method applies to properties representing both predicates and functions.
Rommel N. Carvalho, Kathryn B. Laskey, Paulo C. G. Costa

### Probabilistic Ontology and Knowledge Fusion for Procurement Fraud Detection in Brazil

Abstract
To cope with citizens’ demand for transparency and corruption prevention, the Brazilian Office of the Comptroller General (CGU) has carried out a number of actions, including: awareness campaigns aimed at the private sector; campaigns to educate the public; research initiatives; and regular inspections and audits of municipalities and states. Although CGU has collected information from hundreds of different sources - Revenue Agency, Federal Police, and others - the process of fusing all this data has not been efficient enough to meet the needs of CGU’s decision makers. Therefore, it is natural to change the focus from data fusion to knowledge fusion. As a consequence, traditional syntactic methods should be augmented with techniques that represent and reason with the semantics of databases. However, commonly used approaches, such as Semantic Web technologies, fail to deal with uncertainty, a dominant characteristic in corruption prevention. This paper presents the use of probabilistic ontologies built with Probabilistic OWL (PR-OWL) to design and test a model that performs information fusion to detect possible frauds in procurements involving Federal money in Brazil. To design this model, a recently developed tool for creating PR-OWL ontologies was used with support from PR-OWL specialists and careful guidance from a fraud detection specialist from CGU. At present, the task of procurement fraud detection is done manually by an auditor. The number of suspicious cases that can be analyzed by a single person is small. The experimental results obtained with the presented approach are preliminary, but show the viability of developing a tool based on PR-OWL ontologies to automatize this task. This paper also examplifies how to use PR-OWL 2.0 to provide a link between the deterministic and probabilistic parts of the ontology.
Rommel N. Carvalho, Shou Matsumoto, Kathryn B. Laskey, Paulo C. G. Costa, Marcelo Ladeira, Laécio L. Santos

### Understanding a Probabilistic Description Logic via Connections to First-Order Logic of Probability

Abstract
This paper analyzes the probabilistic description logic P-$$\mathcal{SROIQ}$$ as a fragment of well-known first-order probabilistic logic (FOPL).P-$$\mathcal{SROIQ}$$ was suggested as a language that is capable of representing and reasoning about different kinds of uncertainty in ontologies, namely generic probabilistic relationships between concepts and probabilistic facts about individuals. However, some semantic properties of P-$$\mathcal{SROIQ}$$ have been unclear which raised concerns regarding whether it could be used for representing probabilistic ontologies. In this paper we provide an insight into its semantics by translating P-$$\mathcal{SROIQ}$$ into FOPL with a specific subjective semantics based on possible worlds. We prove faithfulness of the translation and demonstrate the fundamental nature of some limitations of P-$$\mathcal{SROIQ}$$. Finally, we briefly discuss the implications of the exposed semantic properties of the logic on probabilistic modeling.
Pavel Klinov, Bijan Parsia

### Pronto: A Practical Probabilistic Description Logic Reasoner

Abstract
This paper presents Pronto—the first probabilistic Description Logic (DL) reasoner capable of processing knowledge bases containing about a thousand of probabilistic axioms. We describe in detail the novel probabilistic satisfiability (PSAT) algorithm which lies at the heart of Pronto’s architecture. Its key difference from previously developed (propositional) PSAT algorithms is its interaction with the underlying DL reasoner which, first, enables applying well-known linear programming techniques to non-propositional PSAT and, second, is crucial to scaling with respect the amount of classical (non-probabilistic) knowledge. The latter is the key feature for dealing with probabilistic extensions of existing large ontologies. Finally we present the layered architecture of Pronto and demonstrate the experimental evaluation results on randomly generated instances of non-propositional PSAT.
Pavel Klinov, Bijan Parsia

### Instance-Based Non-standard Inferences in $\mathcal{EL}$ with Subjective Probabilities

Abstract
For practical ontology-based applications representing and reasoning with probabilities is an essential task. For Description Logics with subjective probabilities reasoning procedures for testing instance relations based on the completion method have been developed.
In this paper we extend this technique to devise algorithms for solving non-standard inferences for $$\mathcal{EL}$$ and its probabilistic extension Prob- $${\mathcal{EL}^{01}_c}$$: computing the most specific concept of an individual and finding explanations for instance relations.
Rafael Peñaloza, Anni-Yasmin Turhan

### Finite Fuzzy Description Logics and Crisp Representations

Abstract
Fuzzy Description Logics (DLs) are a formalism for the representation of structured knowledge that is imprecise or vague by nature. In fuzzy DLs, restricting to a finite set of degrees of truth has proved to be useful, both for theoretical and practical reasons. In this paper, we propose finite fuzzy DLs as a generalization of existing approaches. We assume a finite totally ordered set of linguistic terms or labels, which is very useful in practice since expert knowledge is usually expressed using linguistic terms. Then, we consider fuzzy DLs based on any smooth t-norm defined over this set. Initially we focus on the finite fuzzy DL $$\mathcal{ALCH}$$, studying some logical properties, and showing the decidability of the logic by presenting a reasoning preserving reduction to the classical case. Finally, we extend our logic in two directions: by considering non-smooth t-norms and by considering additional DL constructors.
Fernando Bobillo, Umberto Straccia

### Reasoning in Fuzzy OWL 2 with DeLorean

Abstract
Classical ontologies are not suitable to represent imprecise or vague information, which has led to several extensions using non-classical logics. In particular, several fuzzy extensions have been proposed in the literature. In this paper, we present the fuzzy ontology reasoner DeLorean, the first to support a fuzzy extension of OWL 2. We discuss how to use it for fuzzy ontology representation and reasoning, and describe some implementation details and optimization techniques. An empirical evaluation demonstrates that these optimizations considerably improve the performance of the reasoner.
Fernando Bobillo, Miguel Delgado, Juan Gómez-Romero

### Dealing with Contradictory Evidence Using Fuzzy Trust in Semantic Web Data

Abstract
Term similarity assessment usually leads to situations where contradictory evidence support has different views concerning the meaning of a concept and how similar it is to other concepts. Human experts can resolve their differences through discussion, whereas ontology mapping systems need to be able to eliminate contradictions before similarity combination can achieve high quality results. In these situations, different similarities represent conflicting ideas about the interpreted meaning of the concepts. Such contradictions can contribute to unreliable mappings, which in turn worsen both the mapping precision and recall. In order to avoid including contradictory beliefs in similarities during the combination process, trust in the beliefs needs to be established and untrusted beliefs should be excluded from the combination. In this chapter, we propose a solution for establishing fuzzy trust to manage belief conflicts using a fuzzy voting model.
Miklos Nagy, Maria Vargas-Vera

### Storing and Querying Fuzzy Knowledge in the Semantic Web Using FiRE

Abstract
An important problem for the success of ontology-based applications is how to provide persistent storage and querying. For that purpose, many RDF tools capable of storing and querying over a knowledge base, have been proposed. Recently, fuzzy extensions to ontology languages have gained considerable attention especially due to their ability to handle vague information. In this paper we investigate on the issue of using classical RDF storing systems in order to provide persistent storing and querying over large scale fuzzy information. To accomplish this we propose a novel way for serializing fuzzy information into RDF triples, thus classical storing systems can be used without any extensions. Additionally, we extend the existing query languages of RDF stores in order to support expressive fuzzy querying services over the stored data. All our extensions have been implemented in FiRE—an expressive fuzzy DL reasoner that supports the language fuzzy-$$\mathcal{SHIN}$$. Finally, the proposed architecture is evaluated using an industrial application scenario about casting for TV commercials and spots.
Nikolaos Simou, Giorgos Stoilos, Giorgos Stamou

### Transforming Fuzzy Description Logic $\mathcal{ALC}_\mathcal{FL}$ into Classical Description Logic $\mathcal{ALCH}$

Abstract
In this paper, we present a satisfiability preserving transformation of the fuzzy Description Logic $$\mathcal{ALC}_\mathcal{FL}$$ into the classical Description Logic $$\mathcal{ALCH}$$. We can use the already existing DL systems to do the reasoning of $$\mathcal{ALC}_\mathcal{FL}$$ by applying the result of this paper. This work is inspired by Straccia, who has transformed the fuzzy Description Logic $$\mathfrak f\mathcal{ALCH}$$ into the classical Description Logic $$\mathcal{ALCH}$$.
Yining Wu

### A Fuzzy Logic-Based Approach to Uncertainty Treatment in the Rule Interchange Format: From Encoding to Extension

Abstract
The Rule Interchange Format (RIF) is a W3C recommendation that allows rules to be exchanged between rule systems. Uncertainty is an intrinsic feature of real world knowledge, hence it is important to take it into account when building logic rule formalisms. However, the set of truth values in the RIF Basic Logic Dialect (RIF-BLD) currently consists of only two values (t and f), although the RIF Framework for Logic Dialects (RIF-FLD) allows for more. In this paper, we first present two techniques of encoding uncertain knowledge and its fuzzy semantics in RIF-BLD presentation syntax. We then propose an extension leading to an Uncertainty Rule Dialect (RIF-URD) to support a direct representation of uncertain knowledge. In addition, rules in Logic Programs (LP) are often used in combination with the other widely-used knowledge representation formalism of the Semantic Web, namely Description Logics (DL), in many application scenarios of the Semantic Web. To prepare DL as well as LP extensions, we present a fuzzy extension to Description Logic Programs (DLP), called Fuzzy DLP, and discuss its mapping to RIF. Such a formalism not only combines DL with LP, as in DLP, but also supports uncertain knowledge representation.
Jidi Zhao, Harold Boley, Jing Dong

### PrOntoLearn: Unsupervised Lexico-Semantic Ontology Generation Using Probabilistic Methods

Abstract
It is well known that manually formalizing a domain is a tedious and cumbersome process. It is constrained by the knowledge acquisition bottleneck. Therefore, many researchers have developed algorithms and systems to help automate the process. Among them are systems that incorporate text corpora in the knowledge acquisition process. Here, we provide a novel method for unsupervised bottom-up ontology generation. It is based on lexico-semantic structures and Bayesian reasoning to expedite the ontology generation process. To illustrate our approach, we provide three examples generating ontologies in diverse domains and validate them using qualitative and quantitative measures. The examples include the description of high-throughput screening data relevant to drug discovery and two custom text corpora. Our unsupervised method produces viable results with sometimes unexpected content. It is complementary to the typical top-down ontology development process. Our approach may therefore also be useful to domain experts.
Saminda Abeyruwan, Ubbo Visser, Vance Lemmon, Stephan Schürer

### Semantic Web Search and Inductive Reasoning

Abstract
Extensive research activities are recently directed towards the Semantic Web as a future form of the Web. Consequently, Web search as the key technology of the Web is evolving towards some novel form of Semantic Web search. A very promising recent such approach is based on combining standard Web pages and search queries with ontological background knowledge, and using standard Web search engines as the main inference motor of Semantic Web search. In this paper, we further enhance this approach to Semantic Web search by the use of inductive reasoning techniques. This adds especially the important ability to handle inconsistencies, noise, and incompleteness, which are all very likely to occur in distributed and heterogeneous environments, such as the Web. We report on a prototype implementation of the new approach and experimental results.
Claudia d’Amato, Nicola Fanizzi, Bettina Fazzinga, Georg Gottlob, Thomas Lukasiewicz

### Ontology Enhancement through Inductive Decision Trees

Abstract
The popularity of ontologies for representing the semantics behind many real-world domains has created a growing pool of ontologies on various topics. Different ontologists, experts, and organizations create a great variety of ontologies, often for narrow application domains. Some of the created ontologies frequently overlap with other ontologies in broader domains if they pertain to the Semantic Web. Sometimes, they model similar or matching theories that may be inconsistent. To assist in the reuse of these ontologies, this paper describes a technique for enriching manually created ontologies by supplementing them with inductively derived rules, and reducing the number of inconsistencies. The derived rules are translated from decision trees with probability measures, created by executing a tree based data mining algorithm over the data being modelled. These rules can be used to revise an ontology in order to extend the ontology with definitions grounded in empirical data, and identify possible similarities between complementary ontologies. We demonstrate the application of our technique by presenting an example, and discuss how various data types may be treated to generalize the semantics of an ontology for a broader application domain.
Bart Gajderowicz, Alireza Sadeghian, Mikhail Soutchanski

### Assertion Prediction with Ontologies through Evidence Combination

Abstract
Following previous works on inductive methods for ABox reasoning, we propose an alternative method for predicting assertions based on the available evidence and the analogical criterion. Once neighbors of a test individual are selected through some distance measures, a combination rule descending from the Dempster-Shafer theory can join together the evidence provided by the various neighbor individuals in order to predict unknown values in a learning problem. We show how to exploit the procedure in the problems of determining unknown class- and role-memberships or fillers for datatype properties which may be the basis for many further ABox inductive reasoning algorithms. This work presents also an empirical evaluation of the method on real ontologies.
Giuseppe Rizzo, Claudia d’Amato, Nicola Fanizzi, Floriana Esposito

### Representing Uncertain Concepts in Rough Description Logics via Contextual Indiscernibility Relations

Abstract
We investigate the modeling of uncertain concepts via rough description logics (RDLs), which are an extension of traditional description logics (DLs) by a mechanism to handle approximate concept definitions via lower and upper approximations of concepts based on a rough-set semantics. This allows to apply RDLs to modeling uncertain knowledge. Since these approximations are ultimately grounded on an indiscernibility relation, we explore possible logical and numerical ways for defining such relations based on the considered knowledge. In particular, we introduce the notion of context, allowing for the definition of specific equivalence relations, which are directly used for lower and upper approximations of concepts. The notion of context also allows for defining similarity measures, which are used for introducing a notion of tolerance in the indiscernibility. Finally, we describe several learning problems in our RDL framework.
Claudia d’Amato, Nicola Fanizzi, Floriana Esposito, Thomas Lukasiewicz

### Efficient Trust-Based Approximate SPARQL Querying of the Web of Linked Data

Abstract
The web of linked data represents a globally distributed dataspace, which can be queried using the SPARQL query language. However, with the growth in size and complexity of the web of linked data, it becomes impractical for the user to know enough about its structure and semantics for the user queries to produce enough answers. Moreover, there is a prevalence of unreliable data which can dominate the query results misleading the users and software agents. These problems are addressed in the paper by making use of ontologies available on the web of linked data to produce approximate results and also by presenting a trust model that associates RDF statements with trust values, which is used to give prominence to trustworthy data. Trustworthy approximate results can be generated by performing the relaxation steps at compile-time leading to the generation of multiple relaxed queries that are sorted in decreasing order of their similarity scores with the original query and executed. During their execution the trust scores of RDF data fetched are computed. However, the relaxed queries generated have conditions in common and we propose that by performing trust-based relaxations on-the-fly at runtime, the shared data between several relaxed queries need not be fetched repeatedly. Thus, the trust-based relaxation steps are integrated with the query execution itself resulting in performance benefits. Further opportunities for optimizations during query execution are identified and are used to prune relaxation steps which do not produce results. The implementation of our approach demonstrates its efficacy.
Kuldeep B. R. Reddy, P. Sreenivasa Kumar

### Backmatter

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