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From Knowledge Graph Embedding to Ontology Embedding: Region Based Representations of Relational Structures

arXiv.org Artificial Intelligence

Recent years have witnessed the enormous success of low-dimensional vector space representations of knowledge graphs to predict missing facts or find erroneous ones. Currently, however, it is not yet well-understood how ontological knowledge, e.g. given as a set of (existential) rules, can be embedded in a principled way. To address this shortcoming, in this paper we introduce a framework based on convex regions, which can faithfully incorporate ontological knowledge into the vector space embedding. Our technical contribution is two-fold. First, we show that some of the most popular existing embedding approaches are not capable of modelling even very simple types of rules. Second, we show that our framework can represent ontologies that are expressed using so-called quasi-chained existential rules in an exact way, such that any set of facts which is induced using that vector space embedding is logically consistent and deductively closed with respect to the input ontology.


Minimal Module Extraction from DL-Lite Ontologies using QBF Solvers

AAAI Conferences

We present a formal framework for (minimal) module extraction based on an abstract notion of inseparability w.r.t. a signature between ontologies. Two instances of this framework are discussed in detail for DL-Lite ontologies: concept inseparability, when ontologies imply the same complex concept inclusions over the signature, and query inseparability, when they give the same answers to existential queries for any instance data over the signature. We demonstrate that different types of corresponding minimal modules for these inseparability relations can be automatically extracted from large-scale DL-Lite ontologies by composing the tractable syntactic locality-based module extraction algorithm with intractable extraction algorithms using the  multi-engine QBF solver AQME. The extracted minimal modules are compared with those obtained using non-logic-based approaches.


Consequence-Driven Reasoning for Horn SHIQ Ontologies

AAAI Conferences

We present a novel reasoning procedure for Horn SHIQ ontologies—SHIQ ontologies that can be translated to the Horn fragment of first-order logic. In contrast to traditional reasoning procedures for ontologies, our procedure does not build models or model representations, but works by deriving new consequent axioms. The procedure is closely related to the so-called completion-based procedure for EL++ ontologies, and can be regarded as an extension thereof. In fact, our procedure is theoretically optimal for Horn SHIQ ontologies as well as for the common fragment of EL++ and SHIQ. A preliminary empirical evaluation of our procedure on large medical ontologies demonstrates a dramatic improvement over existing ontology reasoners. Specifically, our implementation allows the classification of the largest available OWL version of Galen. To the best of our knowledge no other reasoner is able to classify this ontology.


First-Order Rewritability of Temporal Ontology-Mediated Queries

AAAI Conferences

Baader et al., 2013; Borgwardt et al., 2013; Özcep et al., 2013; Klarman and Meyer, 2014] and shown to preserve query Aiming at ontology-based data access over temporal, rewritability. Note, however, that the inability to define temporal in particular streaming data, we design a language of predicates such as Blizzard(x, t) in ontologies leaves the ontology-mediated queries by extending OWL 2 QL burden of encoding them within queries to the user, which and SPARQL with temporal operators, and investigate goes against the OBDA paradigm. Moreover, natural queries rewritability of these queries into two-sorted such as'check if a weather station has been serviced every 24 first-order logic with and PLUS over time.


An Algebra of Lightweight Ontologies

arXiv.org Artificial Intelligence

This paper argues that certain ontology design problems are profitably addressed by treating ontologies as theories and by defining a set of operations that create new ontologies, including their constraints, out of other ontologies. The paper first shows how to use the operations in the context of ontology reuse, how to take advantage of the operations to compare different ontologies, or different versions of an ontology, and how the operations may help design mediated schemas in a bottom up fashion. The core of the paper discusses how to compute the operations for lightweight ontologies and addresses the question of minimizing the set of constraints of a lightweight ontology. Finally, the paper describes an implementation of the operations, as a Prot\'eg\'e plug-in.