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Two Puzzles Concerning Measures of Uncertainty and the Positive Boolean Connectives

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Progress in Artificial Intelligence (EPIA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4874))

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Abstract

The two puzzles are the Lottery Paradox and the Amalgamation Paradox, which both point out difficulties for aggregating uncertain information. A generalization of the lottery paradox is presented and a new form of an amalgamation reversal is introduced. Together these puzzles highlight a difficulty for introducing measures of uncertainty to a variety of logical knowledge representation frameworks. The point is illustrated by contrasting the constraints on solutions to each puzzle with the structural properties of the preferential semantics for non-monotonic logics (System P), and also with systems of normal modal logics. The difficulties illustrate several points of tensions between the aggregation of uncertain information and aggregation according to the monotonically positive Boolean connectives, ∧ and ∨.

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Authors and Affiliations

  1. Artificial Intelligence Center - CENTRIA, Department of Computer Science, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal

    Gregory Wheeler

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  1. Gregory Wheeler
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José Neves Manuel Filipe Santos José Manuel Machado

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Wheeler, G. (2007). Two Puzzles Concerning Measures of Uncertainty and the Positive Boolean Connectives. In: Neves, J., Santos, M.F., Machado, J.M. (eds) Progress in Artificial Intelligence. EPIA 2007. Lecture Notes in Computer Science(), vol 4874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77002-2_15

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  • DOI: https://doi.org/10.1007/978-3-540-77002-2_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77000-8

  • Online ISBN: 978-3-540-77002-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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