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Reasoning with Ontologies

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Abstract

This chapter considers the notion of a formal ontology, which is a conceptual vocabulary equipped with a logical semantics. Three families of knowledge representation and reasoning formalisms that put ontologies at the core of any knowledge base are presented, namely: description logics, conceptual graphs and existential rules. We present the main knowledge constructs and dialects of these families, as well as the main reasoning problems with their complexity. We highlight the relationships between these families and compare them from an expressivity viewpoint.

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Notes

  1. 1.

    In the Semantic Web area, and specifically concerning the OWL language, the term ontology often includes both kinds of knowledge. Hence, it corresponds to our notion of knowledge base.

  2. 2.

    A few undecidable DLs have been studied.

  3. 3.

    http://www.snomed.org/snomed-ct.

  4. 4.

    http://www.omg.org/uml.

  5. 5.

    See http://owl.cs.manchester.ac.uk/tools/list-of-reasoners/ for an up-to-date list of DL reasoners.

  6. 6.

    http://www.lirmm.fr/cogui

  7. 7.

    http://cogitant.sourceforge.net

  8. 8.

    For query answering problems, the distinction between combined and data complexities is often made: data complexity is the complexity with respect to the size of the data (here the fact base), while combined complexity considers all components of the problem (here, the knowledge base and the query).

  9. 9.

    If \(c_{1_i}\) and \(c_{2_i}\) have the same concept type, the obtained node is labelled by the same label as \(h(c_{1_i})\) ; if the type of \(c_{2_i}\) is strictly more specific than the type of \(c_{1_i}\), it may happen that the labels of \(h(c_{1_i})\) and \(c_{2_i}\) are incompatible (with respect to banned types), which points to an inconsistency in the knowledge base; otherwise, the label of the obtained node is the greatest lower bound of both labels: the obtained type is the conjunction of the types of \(h(c_{1_i})\) and \(c_{2_i}\) and the obtained marker is the smallest of both markers.

  10. 10.

    A fact is usually defined as a ground atom. However, in the existential rule setting, a more general notion of a fact can be considered, where a fact is an existentially closed conjunction of atoms, which is in line with the view of a fact as a rule with an empty body. This generalized notion allows one to encode unknown values in a natural way.

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Authors and Affiliations

  1. LIRMM-CNRS and Université de Montpellier- Inria, Montpellier, France

    Meghyn Bienvenu, Michel Leclère & Marie-Laure Mugnier

  2. LIG-CNRS and Université de Grenoble, Grenoble, France

    Marie-Christine Rousset

Authors
  1. Meghyn Bienvenu
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  2. Michel Leclère
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  3. Marie-Laure Mugnier
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  4. Marie-Christine Rousset
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Correspondence to Meghyn Bienvenu .

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Editors and Affiliations

  1. CRIL-CNRS, Université d'Artois and Institut Universitaire de France, Lens, France

    Pierre Marquis

  2. Aix Marseille Université, Université de Toulon, CNRS, LIS, Marseille, France

    Odile Papini

  3. IRIT, CNRS and Université Paul Sabatier, Toulouse, France

    Henri Prade

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Bienvenu, M., Leclère, M., Mugnier, ML., Rousset, MC. (2020). Reasoning with Ontologies. In: Marquis, P., Papini, O., Prade, H. (eds) A Guided Tour of Artificial Intelligence Research. Springer, Cham. https://doi.org/10.1007/978-3-030-06164-7_6

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