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Description Logic, Theory Combination, and All That pp 475–496Cite as

Explaining Axiom Pinpointing

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11560))

Abstract

Axiom pinpointing refers to the task of highlighting (or pinpointing) the axioms in an ontology that are responsible for a given consequence to follow. This is a fundamental task for understanding and debugging very large ontologies. Although the name axiom pinpointing was only coined in 2003, the problem itself has a much older history, even if considering only description logic ontologies. In this work, we try to explain axiom pinpointing: what it is; how it works; how it is solved; and what it is useful for. To answer this questions, we take a historic look at the field, focusing mainly on description logics, and the specific contributions stemming from one researcher, who started it all in more than one sense.

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Notes

  1. 1.

    I am an informal (some will say impolite) Mexican, who insists on using the term Franz when referring to Franz Baader. I will do this often from now on. Please bear with me.

  2. 2.

    We use the infix notation for the consequence relation.

  3. 3.

    I rather prefer the name MinA coined by Franz Baader as we started our work on this topic. However, despite my best efforts, justification has become the de facto standard name in DLs. Even I must admit that it is catchier.

  4. 4.

    In the original paper [5], this was called a clash formula, since it explains the clashes obtained by the algorithm. The name was later changed to pinpointing formula to reflect its more general purpose.

  5. 5.

    I still remember when I managed to construct the first counterexample just before the deadline for submitting the paper. Imagine a scared first-year PhD student interrupting his supervisor’s holidays to tell him the bad news.

  6. 6.

    As a historical remark, an important reason why I ended up working with Franz was because I fell in love with automata theory while I was doing my masters in Dresden. Being the Chair for Automata Theory, it only made sense to ask him for a topic. Little did I know at the time where this would take me.

  7. 7.

    Also known, and herewith referred as Meng.

  8. 8.

    Imagine someone making an insurance claim after having a finger amputated. If the insurer makes this kind of error, they might end of paying a larger lump for an amputated arm.

  9. 9.

    Formally, a repair is a maximal subontology that does not entail the consequence. This is the dual notion of a justification, which is also studied in variations of axiom pinpointing in different fields.

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  1. University of Milano-Bicocca, Milan, Italy

    Rafael Peñaloza

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  2. University of Manchester, Manchester, UK

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  4. TU Dresden, Dresden, Germany

    Anni-Yasmin Turhan

  5. University of Liverpool, Liverpool, UK

    Frank Wolter

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Peñaloza, R. (2019). Explaining Axiom Pinpointing. In: Lutz, C., Sattler, U., Tinelli, C., Turhan, AY., Wolter, F. (eds) Description Logic, Theory Combination, and All That. Lecture Notes in Computer Science(), vol 11560. Springer, Cham. https://doi.org/10.1007/978-3-030-22102-7_22

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