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Simplification Rules for the Coherent Probability Assessment Problem

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Abstract

In this paper we develop a procedure for checking the consistency (coherence) of a partial probability assessment. The general problem (called CPA) is NP-complete, hence, to have a reasonable application some heuristic is needed. Our proposal differs from others because it is based on a skilful use of the logical relations present among the events. In other approaches the consistency problem is reduced directly to the satisfiability of a system of linear constraints. Here, thanks to the characterization of particular configurations and to the elimination of variables, an instance of the problem is reduced to smaller instances. To obtain such results, we introduce a procedure based on rules resembling those given by Davis–Putnam for the satisfiability of Boolean formulas. At the end a particularized description of an actual implementation is given.

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Authors and Affiliations

  1. Dipartimento di Metodi Quantitativi, Università di Siena, Italy

    Marco Baioletti

  2. Dipartimento di Matematica e Informatica, Università di Perugia, Italy

    Andrea Capotorti & Sauro Tulipani

  3. Dipartimento di Metodi e Modelli Matematici, Università “La Sapienza”, Italy

    Barbara Vantaggi

Authors
  1. Marco Baioletti
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  2. Andrea Capotorti
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  3. Sauro Tulipani
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  4. Barbara Vantaggi
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Baioletti, M., Capotorti, A., Tulipani, S. et al. Simplification Rules for the Coherent Probability Assessment Problem. Annals of Mathematics and Artificial Intelligence 35, 11–28 (2002). https://doi.org/10.1023/A:1014585822798

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