Two puzzles concerning measures of uncertainty and the positive Boolean connectives
EPIA'07 Proceedings of the aritficial intelligence 13th Portuguese conference on Progress in artificial intelligence
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A bounded formula is a pair consisting of a propositional formula 驴 in the first coordinate and a real number within the unit interval in the second coordinate, interpreted to express the lower-bound probability of 驴. Converting conjunctive/disjunctive combinations of bounded formulas to a single bounded formula consisting of the conjunction/disjunction of the propositions occurring in the collection along with a newly calculated lower probability is called absorption. This paper introduces two inference rules for effecting conjunctive and disjunctive absorption and compares the resulting logical system, called System Y, to axiom System P. Finally, we demonstrate how absorption resolves the lottery paradox and the paradox of the preference.