Rational Partial Choice Functions and Their Application to Belief Revision

Jianbing Ma, W. Liu, D. Dubois

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Abstract

    Necessary and sufficient conditions for choice functions to be rational have been intensively studied in the past. However, in these attempts, a choice function is completely specified. That is, given any subset of options, called an issue, the best option over that issue is always known, whilst in real-world scenarios, it is very often that only a few choices are known instead of all. In this paper, we study partial choice functions and investigate necessary and sufficient rationality conditions for situations where only a few choices are known. We prove that our necessary and sufficient condition for partial choice functions boils down to the necessary and sufficient conditions for complete choice functions proposed in the literature. Choice functions have been instrumental in belief revision theory. That is, in most approaches to belief revision, the problem studied can simply be described as the choice of possible worlds compatible with the input information, given an agent’s prior belief state. The main effort has been to devise strategies in order to infer the agents revised belief state. Our study considers the converse problem: given a collection of input information items and their corresponding revision results (as provided by an agent), does there exist a rational revision operation used by the agent and a consistent belief state that may explain the observed results?
    Original languageEnglish
    Title of host publicationKnowledge Science, Engineering and Management
    EditorsSongmao Zhang, Martin Wirsing, Zili Zhang
    Place of PublicationSwitzerland
    PublisherSpringer Verlag
    Pages128-140
    Volume9403
    ISBN (Print)Online: 978-3-319-25159-2, Print: 978-3-319-25158-5
    DOIs
    Publication statusPublished - 3 Nov 2015

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