From fuzzy to annotated semantic web languages

The aim of this chapter is to present a detailed, selfcontained and comprehensive account of the state of the art in representing and reasoning with fuzzy knowledge in Semantic Web Languages such as triple languages RDF/RDFS, conceptual languages of the OWL 2 family and rule languages. We further show how one may generalise them to so-called annotation domains, that cover also e.g. temporal and provenance extensions

Quantitative Methods for Similarity in Description Logics

Description Logics (DLs) are a family of logic-based knowledge representation languages used to describe the knowledge of an application domain and reason about it in formally well-defined way. They allow users to describe the important notions and classes of the knowledge domain as concepts, which formalize the necessary and sufficient conditions for individual objects to belong to that concept. A variety of different DLs exist, differing in the set of properties one can use to express concepts, the so-called concept constructors, as well as the set of axioms available to describe the relations between concepts or individuals. However, all classical DLs have in common that they can only express exact knowledge, and correspondingly only allow exact inferences. Either we can infer that some individual belongs to a concept, or we can't, there is no in-between. In practice though, knowledge is rarely exact. Many definitions have their exceptions or are vaguely formulated in the first place, and people might not only be interested in exact answers, but also in alternatives that are "close enough". This thesis is aimed at tackling how to express that something "close enough", and how to integrate this notion into the formalism of Description Logics. To this end, we will use the notion of similarity and dissimilarity measures as a way to quantify how close exactly two concepts are. We will look at how useful measures can be defined in the context of DLs, and how they can be incorporated into the formal framework in order to generalize it. In particular, we will look closer at two applications of thus measures to DLs: Relaxed instance queries will incorporate a similarity measure in order to not just give the exact answer to some query, but all answers that are reasonably similar. Prototypical definitions on the other hand use a measure of dissimilarity or distance between concepts in order to allow the definitions of and reasoning with concepts that capture not just those individuals that satisfy exactly the stated properties, but also those that are "close enough"

Current and Future Challenges in Knowledge Representation and Reasoning

Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as machine learning and reasoning under uncertainty. In July 2022 a Dagstuhl Perspectives workshop was held on Knowledge Representation and Reasoning. The goal of the workshop was to describe the state of the art in the field, including its relation with other areas, its shortcomings and strengths, together with recommendations for future progress. We developed this manifesto based on the presentations, panels, working groups, and discussions that took place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge Representation: its origins, goals, milestones, and current foci; its relation to other disciplines, especially to Artificial Intelligence; and on its challenges, along with key priorities for the next decade

Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic

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

Semantic-guided predictive modeling and relational learning within industrial knowledge graphs

The ubiquitous availability of data in today’s manufacturing environments, mainly driven by the extended usage of software and built-in sensing capabilities in automation systems, enables companies to embrace more advanced predictive modeling and analysis in order to optimize processes and usage of equipment. While the potential insight gained from such analysis is high, it often remains untapped, since integration and analysis of data silos from different production domains requires high manual effort and is therefore not economic. Addressing these challenges, digital representations of production equipment, so-called digital twins, have emerged leading the way to semantic interoperability across systems in different domains. From a data modeling point of view, digital twins can be seen as industrial knowledge graphs, which are used as semantic backbone of manufacturing software systems and data analytics. Due to the prevalent historically grown and scattered manufacturing software system landscape that is comprising of numerous proprietary information models, data sources are highly heterogeneous. Therefore, there is an increasing need for semi-automatic support in data modeling, enabling end-user engineers to model their domain and maintain a unified semantic knowledge graph across the company. Once the data modeling and integration is done, further challenges arise, since there has been little research on how knowledge graphs can contribute to the simplification and abstraction of statistical analysis and predictive modeling, especially in manufacturing. In this thesis, new approaches for modeling and maintaining industrial knowledge graphs with focus on the application of statistical models are presented. First, concerning data modeling, we discuss requirements from several existing standard information models and analytic use cases in the manufacturing and automation system domains and derive a fragment of the OWL 2 language that is expressive enough to cover the required semantics for a broad range of use cases. The prototypical implementation enables domain end-users, i.e. engineers, to extend the basis ontology model with intuitive semantics. Furthermore it supports efficient reasoning and constraint checking via translation to rule-based representations. Based on these models, we propose an architecture for the end-user facilitated application of statistical models using ontological concepts and ontology-based data access paradigms. In addition to that we present an approach for domain knowledge-driven preparation of predictive models in terms of feature selection and show how schema-level reasoning in the OWL 2 language can be employed for this task within knowledge graphs of industrial automation systems. A production cycle time prediction model in an example application scenario serves as a proof of concept and demonstrates that axiomatized domain knowledge about features can give competitive performance compared to purely data-driven ones. In the case of high-dimensional data with small sample size, we show that graph kernels of domain ontologies can provide additional information on the degree of variable dependence. Furthermore, a special application of feature selection in graph-structured data is presented and we develop a method that allows to incorporate domain constraints derived from meta-paths in knowledge graphs in a branch-and-bound pattern enumeration algorithm. Lastly, we discuss maintenance of facts in large-scale industrial knowledge graphs focused on latent variable models for the automated population and completion of missing facts. State-of-the art approaches can not deal with time-series data in form of events that naturally occur in industrial applications. Therefore we present an extension of learning knowledge graph embeddings in conjunction with data in form of event logs. Finally, we design several use case scenarios of missing information and evaluate our embedding approach on data coming from a real-world factory environment. We draw the conclusion that industrial knowledge graphs are a powerful tool that can be used by end-users in the manufacturing domain for data modeling and model validation. They are especially suitable in terms of the facilitated application of statistical models in conjunction with background domain knowledge by providing information about features upfront. Furthermore, relational learning approaches showed great potential to semi-automatically infer missing facts and provide recommendations to production operators on how to keep stored facts in synch with the real world

Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic