Revisiting Chase Termination for Existential Rules and their Extension to Nonmonotonic Negation

Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology- Based Data Access. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure the termination of a breadth-first forward chaining algorithm known as the chase. Several variants of the chase have been proposed. In the first part of this paper, we propose a new tool that allows to extend existing acyclicity conditions ensuring chase termination, while keeping good complexity properties. In the second part, we study the extension to existential rules with nonmonotonic negation under stable model semantics, discuss the relevancy of the chase variants for these rules and further extend acyclicity results obtained in the positive case.Comment: This paper appears in the Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014

Existential Rule Languages with Finite Chase: Complexity and Expressiveness

Finite chase, or alternatively chase termination, is an important condition to ensure the decidability of existential rule languages. In the past few years, a number of rule languages with finite chase have been studied. In this work, we propose a novel approach for classifying the rule languages with finite chase. Using this approach, a family of decidable rule languages, which extend the existing languages with the finite chase property, are naturally defined. We then study the complexity of these languages. Although all of them are tractable for data complexity, we show that their combined complexity can be arbitrarily high. Furthermore, we prove that all the rule languages with finite chase that extend the weakly acyclic language are of the same expressiveness as the weakly acyclic one, while rule languages with higher combined complexity are in general more succinct than those with lower combined complexity.Comment: Extended version of a paper to appear on AAAI 201

A rule-based ontological framework for the classification of molecules

BACKGROUND: A variety of key activities within life sciences research involves integrating and intelligently managing large amounts of biochemical information. Semantic technologies provide an intuitive way to organise and sift through these rapidly growing datasets via the design and maintenance of ontology-supported knowledge bases. To this end, OWL-a W3C standard declarative language- has been extensively used in the deployment of biochemical ontologies that can be conveniently organised using the classification facilities of OWL-based tools. One of the most established ontologies for the chemical domain is ChEBI, an open-access dictionary of molecular entities that supplies high quality annotation and taxonomical information for biologically relevant compounds. However, ChEBI is being manually expanded which hinders its potential to grow due to the limited availability of human resources. RESULTS: In this work, we describe a prototype that performs automatic classification of chemical compounds. The software we present implements a sound and complete reasoning procedure of a formalism that extends datalog and builds upon an off-the-shelf deductive database system. We capture a wide range of chemical classes that are not expressible with OWL-based formalisms such as cyclic molecules, saturated molecules and alkanes. Furthermore, we describe a surface 'less-logician-like' syntax that allows application experts to create ontological descriptions of complex biochemical objects without prior knowledge of logic. In terms of performance, a noticeable improvement is observed in comparison with previous approaches. Our evaluation has discovered subsumptions that are missing from the manually curated ChEBI ontology as well as discrepancies with respect to existing subclass relations. We illustrate thus the potential of an ontology language suitable for the life sciences domain that exhibits a favourable balance between expressive power and practical feasibility. CONCLUSIONS: Our proposed methodology can form the basis of an ontology-mediated application to assist biocurators in the production of complete and error-free taxonomies. Moreover, such a tool could contribute to a more rapid development of the ChEBI ontology and to the efforts of the ChEBI team to make annotated chemical datasets available to the public. From a modelling point of view, our approach could stimulate the adoption of a different and expressive reasoning paradigm based on rules for which state-of-the-art and highly optimised reasoners are available; it could thus pave the way for the representation of a broader spectrum of life sciences and biomedical knowledge.</p