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

Converting Instance Checking to Subsumption: A Rethink for Object Queries over Practical Ontologies

Efficiently querying Description Logic (DL) ontologies is becoming a vital task in various data-intensive DL applications. Considered as a basic service for answering object queries over DL ontologies, instance checking can be realized by using the most specific concept (MSC) method, which converts instance checking into subsumption problems. This method, however, loses its simplicity and efficiency when applied to large and complex ontologies, as it tends to generate very large MSC's that could lead to intractable reasoning. In this paper, we propose a revision to this MSC method for DL SHI, allowing it to generate much simpler and smaller concepts that are specific-enough to answer a given query. With independence between computed MSC's, scalability for query answering can also be achieved by distributing and parallelizing the computations. An empirical evaluation shows the efficacy of our revised MSC method and the significant efficiency achieved when using it for answering object queries

A Machine Learning Approach for Optimizing Heuristic Decision-making in OWL Reasoners

Description Logics (DLs) are formalisms for representing knowledge bases of application domains. TheWeb Ontology Language (OWL) is a syntactic variant of a very expressive description logic. OWL reasoners can infer implied information from OWL ontologies. The performance of OWL reasoners can be severely affected by situations that require decision-making over many alternatives. Such a non-deterministic behavior is often controlled by heuristics that are based on insufficient information. This thesis proposes a novel OWL reasoning approach that applies machine learning (ML) to implement pragmatic and optimal decision-making strategies in such situations. Disjunctions occurring in ontologies are one source of non deterministic actions in reasoners. We propose two ML-based approaches to reduce the non-determinism caused by dealing with disjunctions. The first approach is restricted to propositional description logic while the second one can deal with standard description logic. The first approach builds a logistic regression classifier that chooses a proper branching heuristic for an input ontology. Branching heuristics are first developed to help Propositional Satisfiability (SAT) based solvers with making decisions about which branch to pick in each branching level. The second approach is the developed version of the first approach. An SVM (Support Vector Machine) classier is designed to select an appropriate expansion-ordering heuristic for an input ontology. The built-in heuristics are designed for expansion ordering of satisfiability testing in OWL reasoners. They determine the order for branches in search trees. Both of the above approaches speed up our ML-based reasoner by up to two orders of magnitude in comparison to the non-ML reasoner. Another source of non-deterministic actions is the order in which tableau rules should be applied. On average, our ML-based approach that is an SVM classifier achieves a speedup of two orders of magnitude when compared to the most expensive rule ordering of the non-ML reasoner

Design and Evaluation of Algorithms for Parallel Classification of Ontologies

Description Logics are a family of knowledge representation formalisms with formal semantics. In recent years, DLs have influenced the design and standardization of the Web Ontology Language OWL. The acceptance of OWL as a web standard has promoted the widespread utilization of DL ontologies on the web. One of the most frequently used inference services of description logic reasoners classifies all named classes of OWL ontologies into a subsumption hierarchy. Due to emerging OWL ontologies from the web community consisting of up to hundreds of thousand of named classes and the increasing availability of multi-processor and multi- or many-core computers, the need for parallelizing description logic inference services to achieve a better scalability is expected. The contribution of this thesis has two aspects. On a theoretical level, it first presents algorithms to construct a TBox in parallel, which are independent of a particular DL logic, however they sacrifice completeness. Then, a sound and complete algorithm for TBox classification in parallel is presented. In this algorithm all the subsumption relationships between concepts of a partition assigned to a single thread are found correctly, in other words, correctness of the TBox subsumption hierarchy is guaranteed. Thereafter, we provide an extension of the sound and complete algorithm which is used to handle TBox classification concurrently and more efficiently. This thesis also describes an optimization technique suitable for better partitioning the list of concepts to be inserted into the TBox. On a practical level, a running prototype, Parallel TBox Classifier was implemented for each generation of the classifier based on the above theoretical foundations, respectively. The Parallel TBox Classifier is used to evaluate the practical merit of the proposed algorithms as well as the effectiveness of the designed optimizations against existing state-of-the-art benchmarks. The empirical results illustrate that Parallel TBox Classifier outperforms the Sequential TBox Classifier on real world ontologies with a linear or superlinear speedup factor. Parallel TBox Classifier can form a basis to develop more efficient parallel classification techniques for real world ontologies with different sizes and DL complexities

Parallelizing Description Logic Reasoning

Description Logic has become one of the primary knowledge representation and reasoning methodologies during the last twenty years. A lot of areas are benefiting from description logic based technologies. Description logic reasoning algorithms and a number of optimization techniques for them play an important role and have been intensively researched. However, few of them have been systematically investigated in a concurrency context in spite of multi-processor computing facilities growing up. Meanwhile, semantic web, an application domain of description logic, is producing vast knowledge data on the Internet, which needs to be dealt with by using scalable solutions. This situation requires description logic reasoners to be endowed with reasoning scalability. This research introduced concurrent computing in two aspects: classification, and tableau-based description logic reasoning. Classification is a core description logic reasoning service. Over more than two decades many research efforts have been devoted to optimizing classification. Those classification optimization algorithms have shown their pragmatic effectiveness for sequential processing. However, as concurrent computing becomes widely available, new classification algorithms that are well suited to parallelization need to be developed. This need is further supported by the observation that most available OWL reasoners, which are usually based on tableau reasoning, can only utilize a single processor. Such an inadequacy often leads users working in ontology development to frustration, especially if their ontologies are complex and require long processing times. Classification service finds out all named concept subsumption relationships entailed in a knowledge base. Each subsumption test enrolls two concepts and is independent of the others. At most n^2 subsumption tests are needed for a knowledge base which contains n concepts. As the first contribution of this research, we developed an algorithm and a corresponding architecture showing that reasoning scalability can be gained by using concurrent computing. Further, this research investigated how concurrent computing can increase performance of tableau-based description logic reasoning algorithms. Tableau-based description logic reasoning decides a problem by constructing an AND-OR tree. Before this research, some research has shown the effectiveness of parallelizing processing disjunction branches of a tableau expansion tree. Our research has shown how reasoning scalability can be gained by processing conjunction branches of a tableau expansion tree. In addition, this research developed an algorithm, merge classification, that uses a divide and conquer strategy for parallelizing classification. This method applies concurrent computing to the more efficient classification algorithm, top-search & bottom-search, which has been adopted as a standard procedure for classification. Reasoning scalability can be observed in a number of real world cases by using this algorithm

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

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

Fuzzy Description Logics with General Concept Inclusions

Description logics (DLs) are used to represent knowledge of an application domain and provide standard reasoning services to infer consequences of this knowledge. However, classical DLs are not suited to represent vagueness in the description of the knowledge. We consider a combination of DLs and Fuzzy Logics to address this task. In particular, we consider the t-norm-based semantics for fuzzy DLs introduced by Hájek in 2005. Since then, many tableau algorithms have been developed for reasoning in fuzzy DLs. Another popular approach is to reduce fuzzy ontologies to classical ones and use existing highly optimized classical reasoners to deal with them. However, a systematic study of the computational complexity of the different reasoning problems is so far missing from the literature on fuzzy DLs. Recently, some of the developed tableau algorithms have been shown to be incorrect in the presence of general concept inclusion axioms (GCIs). In some fuzzy DLs, reasoning with GCIs has even turned out to be undecidable. This work provides a rigorous analysis of the boundary between decidable and undecidable reasoning problems in t-norm-based fuzzy DLs, in particular for GCIs. Existing undecidability proofs are extended to cover large classes of fuzzy DLs, and decidability is shown for most of the remaining logics considered here. Additionally, the computational complexity of reasoning in fuzzy DLs with semantics based on finite lattices is analyzed. For most decidability results, tight complexity bounds can be derived

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book