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

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

Truth maintenance in knowledge-based systems

Truth Maintenance Systems (TMS) have been applied in a wide range of domains, from diagnosing electric circuits to belief revision in agent systems. There also has been work on using the TMS in modern Knowledge-Based Systems such as intelligent agents and ontologies. This thesis investigates the applications of TMSs in such systems. For intelligent agents, we use a “light-weight” TMS to support query caching in agent programs. The TMS keeps track of the dependencies between a query and the facts used to derive it so that when the agent updates its database, only affected queries are invalidated and removed from the cache. The TMS employed here is “light-weight” as it does not maintain all intermediate reasoning results. Therefore, it is able to reduce memory consumption and to improve performance in a dynamic setting such as in multi-agent systems. For ontologies, this work extends the Assumption-based Truth Maintenance System (ATMS) to tackle the problem of axiom pinpointing and debugging in ontology-based systems with different levels of expressivity. Starting with finding all errors in auto-generated ontology mappings using a “classic” ATMS [23], we extend the ATMS to solve the axiom pinpointing problem in Description Logics-based Ontologies. We also attempt this approach to solve the axiom pinpointing problem in a more expressive upper ontology, SUMO, whose underlying logic is undecidable

Coupling tableau algorithms for expressive description logics with completion-based saturation procedures

Abstract. Nowadays, saturation-based reasoners for the OWL EL profile are able to handle large ontologies such as SNOMED very efficiently. However, saturation-based reasoning procedures become incomplete if the ontology is extended with axioms that use features of more expressive Description Logics, e.g., disjunctions. Tableau-based procedures, on the other hand, are not limited to a specific OWL profile, but even highly optimised reasoners might not be efficient enough to handle large ontologies such as SNOMED. In this paper, we present an approach for tightly coupling tableau-and saturation-based procedures that we implement in the OWL DL reasoner Konclude. Our detailed evaluation shows that this combination significantly improves the reasoning performance on a wide range of ontologies