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On the Linear Structure of Betting Criterion and the Checking of Coherence

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Abstract

We use imprecise probabilities, based on a concept of generalized coherence, for the management of uncertainty in artificial intelligence. With the aim of reducing the computational difficulties, in the checking of generalized coherence we propose a method which exploits, in the framework of the betting criterion, suitable subsets of the sets of values of the random gains. We give an algorithm in each step of which a linear system with a reduced number of unknowns can be used. Our method improves a procedure already existing in literature and could be integrated with recent approaches of other authors, who exploit suitable logical conditions with the aim of splitting the problem into subproblems. We remark that our approach could be also used in combination with efficient methods like column generation techniques. Finally, to illustrate our method, we give some examples.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Viale A. Doria, 6-95125, Catania, Italy

    Veronica Biazzo

  2. Dipartimento di Metodi e Modelli Matematici, Via A. Scarpa, 16-00161, Roma, Italy

    Angelo Gilio

Authors
  1. Veronica Biazzo
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  2. Angelo Gilio
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Biazzo, V., Gilio, A. On the Linear Structure of Betting Criterion and the Checking of Coherence. Annals of Mathematics and Artificial Intelligence 35, 83–106 (2002). https://doi.org/10.1023/A:1014570831884

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