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Forgetting-Based Inconsistency Measure

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Scalable Uncertainty Management (SUM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9858))

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Abstract

We propose to apply a variant of forgetting, a simple method to restore consistency, in order to get a new inconsistency measure from the following intuitive idea: How much effort is needed to restore consistency of a knowledge base is presumably indicative of how inconsistent the knowledge base is. We discuss properties of the inconsistency measure obtained, in particular in the face of well-known postulates for inconsistency measures. We also mention in what sense this new measure does not fall into the dichotomy of inconsistency measures proposed in the literature: alphabet-based approaches vs formula-based approaches.

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Notes

  1. 1.

    As to labelling, logical constants \(\top \) and \(\bot \) are not considered atoms: A formula in which either occurs is regarded as labelled if all other atoms in it are superscripted.

  2. 2.

    That is, if \(\varphi \) is unlabelled, it is identified with \(\varphi (v^{1}_1,\ldots ,v^{i_1}_1,\ldots ,v^{1}_p,\ldots ,v^{i_p}_p)\) where \(v_1,\ldots ,v_p\) are all the propositional variables in \(\varphi \).

  3. 3.

    A formula \(\varphi \) is free for \(\varGamma \) iff \(\varDelta \cup \{\varphi \} \vdash \bot \) for no consistent subset \(\varDelta \) of \(\varGamma \).

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Acknowledgements

The author is grateful to the reviewers for both useful comments on this paper and insightful suggestions about this topic.

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Authors and Affiliations

  1. IRIT, CNRS, Université Paul Sabatier, 118 route de Narbonne, F-31062, Toulouse Cedex, France

    Philippe Besnard

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  1. Philippe Besnard
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Correspondence to Philippe Besnard .

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Editors and Affiliations

  1. Cardiff University , Cardiff, United Kingdom

    Steven Schockaert

  2. Télécom ParisTech , Paris, Paris, France

    Pierre Senellart

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Besnard, P. (2016). Forgetting-Based Inconsistency Measure. In: Schockaert, S., Senellart, P. (eds) Scalable Uncertainty Management. SUM 2016. Lecture Notes in Computer Science(), vol 9858. Springer, Cham. https://doi.org/10.1007/978-3-319-45856-4_23

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  • DOI: https://doi.org/10.1007/978-3-319-45856-4_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45855-7

  • Online ISBN: 978-3-319-45856-4

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