Decidability of ALCP(D) for concrete domains with the EHD-property

Reasoning for Description logics with concrete domains and w.r.t. general TBoxes easily becomes undecidable. For particular, restricted concrete domains decidablity can be regained. We introduce a novel way to integrate a concrete domain D into the well-known description logic ALC, we call the resulting logic ALCP(D). We then identify sufficient conditions on D that guarantee decidability of the satisfiability problem, even in the presence of general TBoxes. In particular, we show decidability of ALCP(D) for several domains over the integers, for which decidability was open. More generally, this result holds for all negation-closed concrete domains with the EHD-property, which stands for the existence of a homomorphism is definable. Such technique has recently been used to show decidability of CTL with local constraints over the integers

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

Action, Time and Space in Description Logics

Description Logics (DLs) are a family of logic-based knowledge representation (KR) formalisms designed to represent and reason about static conceptual knowledge in a semantically well-understood way. On the other hand, standard action formalisms are KR formalisms based on classical logic designed to model and reason about dynamic systems. The largest part of the present work is dedicated to integrating DLs with action formalisms, with the main goal of obtaining decidable action formalisms with an expressiveness significantly beyond propositional. To this end, we offer DL-tailored solutions to the frame and ramification problem. One of the main technical results is that standard reasoning problems about actions (executability and projection), as well as the plan existence problem are decidable if one restricts the logic for describing action pre- and post-conditions and the state of the world to decidable Description Logics. A smaller part of the work is related to decidable extensions of Description Logics with concrete datatypes, most importantly with those allowing to refer to the notions of space and time