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Nonmonotonic reasoning with multiple belief sets

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Abstract

In complex reasoning tasks it is often the case that there is no single, correct set of conclusions given some initial information. Instead, there may be several such conclusion sets, which we will call belief sets. In the present paper we introduce nonmonotonic belief set operators and selection operators to formalize and to analyze structural aspects of reasoning with multiple belief sets. We define and investigate formal properties of belief set operators as absorption, congruence, supradeductivity and weak belief monotony. Furthermore, it is shown that for each belief set operator satisfying strong belief cumulativity there exists a largest monotonic logic underlying it, thus generalizing a result for nonmonotonic inference operations. Finally, we study abstract properties of selection operators connected to belief set operators, which are used to choose some of the possible belief sets.

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Authors and Affiliations

  1. Faculty of Sciences, Department of Artificial Intelligence, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    Joeri Engelfriet

  2. Department of Computer Science, Augustplatz, University of Leipzig, 10-11, 04109, Leipzig, Germany

    Heinrich Herre

  3. Faculty of Sciences, Department of Artificial Intelligence, Vrije, Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    Jan Treur

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  1. Joeri Engelfriet
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  2. Heinrich Herre
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  3. Jan Treur
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Engelfriet, J., Herre, H. & Treur, J. Nonmonotonic reasoning with multiple belief sets. Annals of Mathematics and Artificial Intelligence 24, 225–248 (1998). https://doi.org/10.1023/A:1018909517931

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