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Kinetic Consistency and Relevance in Belief Revision

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Logics in Artificial Intelligence (JELIA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10021))

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Abstract

A critical aspect of rational belief revision that has been neglected by the classical AGM framework is what we call the principle of kinetic consistency. Loosely speaking, this principle dictates that the revision policies employed by a rational agent at different belief sets, are not independent, but ought to be related in a certain way. We formalise kinetic consistency axiomatically and semantically, and we establish a representation result explicitly connecting the two. We then combine the postulates for kinetic consistency, with Parikh’s postulate for relevant change, and add them to the classical AGM postulates for revision; we call this augmented set the extended AGM postulates. We prove the consistency and demonstrate the scope of the extended AGM postulates by showing that a whole new class of concrete revision operators introduced hererin, called PD operators, satisfies all extended AGM postulates. PD operators are of interest in their own right as they are natural generalisations of Dalal’s revision operator. We conclude the paper with some examples illustrating the strength of the extended AGM postulates, even for iterated revision scenarios.

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Notes

  1. 1.

    In fact in [9], Parikh conjectured that no classical AGM revision function survives (wP). This was later refuted in [11].

  2. 2.

    To be precise, Katsuno and Mendelzon represent an agent’s beliefs by a sentence rather than a theory. Hence they assign preorders to sentences rather than to theories. We use theories in order to adhere more closely to the original AGM approach. Since we deal only with languages built over finitely many variables, the difference is immaterial.

  3. 3.

    A partition \(Q'\) refines another partition Q, iff for every \(Q'_i \in Q'\) there is \(Q_j \in Q\), such that \(Q'_i \subseteq Q_j\).

  4. 4.

    Since is a total preorder and \([K]\) is finite (because P is assumed to be finite), such a minimal element always exists.

  5. 5.

    To see that such a world indeed exists, consider the sentence \(\varphi \) defined as the conjunction of all literals in \(r\) that are built from variables in \(P-{{ Diff}}( K,r )\). Clearly then, \(r\,\models \, \psi \). Moreover, \(\lnot \psi \not \in K\), for otherwise \({{ Diff}}( K,r )\) would include variables from \(P-{{ Diff}}( K,r )\), which is of course a contradiction. Hence there is a \(u\in [K]\) such that \(u\,\models \, \psi \). By the construction of \(\psi \) it follows that \(u\) agrees with \(r\) on all variables outside \({{ Diff}}( K,r )\).

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Acknowledgements

We are grateful to Fanis Aravanis and to the anonymous reviewers for valuable comments on this work.

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Authors and Affiliations

  1. Department of Business Administration, University of Patras, Patras, Greece

    Pavlos Peppas

  2. QCIS, Faculty of Engineering and IT, University of Technology Sydney, Ultimo, Australia

    Pavlos Peppas & Mary-Anne Williams

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  1. Pavlos Peppas
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  2. Mary-Anne Williams
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Correspondence to Pavlos Peppas .

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Editors and Affiliations

  1. Open University of Cyprus, Nicosia, Cyprus

    Loizos Michael

  2. University of Cyprus, Nicosia, Cyprus

    Antonis Kakas

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Peppas, P., Williams, MA. (2016). Kinetic Consistency and Relevance in Belief Revision. In: Michael, L., Kakas, A. (eds) Logics in Artificial Intelligence. JELIA 2016. Lecture Notes in Computer Science(), vol 10021. Springer, Cham. https://doi.org/10.1007/978-3-319-48758-8_26

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  • DOI: https://doi.org/10.1007/978-3-319-48758-8_26

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