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Main Issues in Belief Revision, Belief Merging and Information Fusion

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Abstract

This chapter focuses on the dynamics of information represented in logical or numerical formats, from pioneering works to recent developments. The logical approach to belief change is a topic that has been extensively studied in Artificial Intelligence, starting in the mid-seventies. In this problem, logical formulas represent beliefs held by an intelligent agent that must be revised upon receiving new information that conflicts with prior beliefs and usually has priority over them. In contrast, in the merging problem, the logical theories that must be combined have equal priority. Such logical approaches recalled here make sense for merging beliefs as well as goals, even if each of these problems cannot be reduced to the other. In the last part, we discuss a number of issues pertaining to the fusion and the revision of uncertainty functions representing epistemic states, such as probability measures, possibility measures and belief functions. The need to cope with logical inconsistency plays a major role in these problems. The ambition of this chapter is not to provide an exhaustive bibliography, but rather to propose an overview of basic notions, main results and new research issues in this area.

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Notes

  1. 1.

    Logical formulas and their logical consequences.

  2. 2.

    However, methods for inconsistency management are surveyed at a more general level in chapter “Argumentation and Inconsistency-Tolerant Reasoning” of this volume.

  3. 3.

    Also called priority to new information.

  4. 4.

    \(K + \alpha = Cn(K\cup \{\alpha \})\). Besides \(K_\bot \) denotes an inconsistent theory.

  5. 5.

    This postulate is omitted if formulas are replaced by their sets of models.

  6. 6.

    It is reduced to \(\{K\}\) if K is consistent with \(\alpha \).

  7. 7.

    Since it is a semantic approach, this pre-order does not depend on the syntactic form of the formula.

  8. 8.

    Within the AGM approach, the epistemic state is attached to a theory K and its revision. Here the theory \(Bel(\varPsi )\) is dictated by the epistemic state \(\le _{\varPsi }\). Its models are the minimal interpretations of \(\le _{\varPsi }\).

  9. 9.

    One can note that C3 and C4 are consequences of these postulates.

  10. 10.

    When there is no constraint, we state \(\mu = \top \), i. e. \(\mu \) is a tautology.

  11. 11.

    For the infinite case, see Chacón and Pino Pérez (2006).

  12. 12.

    In fact, a pseudo-distance satisfying \(d(\omega ,\omega ')=d(\omega ',\omega )\), and \(d(\omega ,\omega ')=0\) if and only if \(\omega =\omega '\) is sufficient, because triangular inequality is not required.

  13. 13.

    So this approach is no longer typically semantic: every base \(K_{i}\) could be seen as a (sub-)profile.

  14. 14.

    Each formula may represent a base, if we want compare with merging within the propositional setting.

  15. 15.

    For a more precise presentation of logic programs and the semantics of stable models, see chapter “Logic Programming” of Volume 2.

  16. 16.

    Originally called ordinal conditional functions (OCF).

  17. 17.

    It stands for \(N(Mod(\mu )) = 1\) where \(Mod(\mu )\) is the set of models of formula \(\mu \).

  18. 18.

    Notice that such probabilities are attached to sources.

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Authors and Affiliations

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

    Didier Dubois

  2. CRIStAL-CNRS, Université de Lille, Lille, France

    Patricia Everaere

  3. CRIL-CNRS, Université d’Artois, Lens, France

    Sébastien Konieczny

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

    Odile Papini

Authors
  1. Didier Dubois
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  2. Patricia Everaere
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  3. Sébastien Konieczny
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  4. Odile Papini
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Correspondence to Didier Dubois .

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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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Dubois, D., Everaere, P., Konieczny, S., Papini, O. (2020). Main Issues in Belief Revision, Belief Merging and Information Fusion. 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_14

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