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Two puzzles concerning measures of uncertainty and the positive Boolean connectives
2007
greg:epia07
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, $\wedge$ and $\vee$.
In proceedings
Gregory Wheeler
José Neves, Manuel Santos, José Machado
Progress in Artificial Intelligence (EPIA 2007)
LNAI
Springer
Berlin
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170-180
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-
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Gregory Wheeler, Two puzzles concerning measures of uncertainty and the positive Boolean connectives, in: José Neves and Manuel Santos and José Machado (eds), Progress in Artificial Intelligence (EPIA 2007), LNAI, Springer, Berlin, Pag. 170-180, 2007.
<a href="/people/members/view.php?code=768e30c2109e32d4ad41104cf0167777" class="author">Gregory Wheeler</a>, <b>Two puzzles concerning measures of uncertainty and the positive Boolean connectives</b>, in: José Neves, Manuel Santos and José Machado (eds), <u>Progress in Artificial Intelligence (EPIA 2007)</u>, LNAI, <a href="http://www.springer.com" title="Link to external entity..." target="_blank" class="publisher">Springer</a>, Berlin, Pag. 170-180, 2007.
@inproceedings {greg:epia07, author = {Gregory Wheeler}, editor = {Jos{\'e} Neves and Manuel Santos and Jos{\'e} Machado}, title = {Two puzzles concerning measures of uncertainty and the positive Boolean connectives}, booktitle = {Progress in Artificial Intelligence (EPIA 2007)}, series = {LNAI}, publisher = {Springer}, address = {Berlin}, pages = {170-180}, 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, $\wedge$ and $\vee$.}, year = {2007}, }
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