Authors
Gregory Wheeler
Frankfurt School Of Finance And Management
Abstract
A bounded formula is a pair consisting of a propositional formula φ in the first coordinate and a real number within the unit interval in the second coordinate, interpreted to express the lower-bound probability of φ. 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.
Keywords probabilistic logic  rational acceptance  the lottery paradox  System P  bounded uncertain reasoning
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DOI 10.1007/s10849-005-9006-6
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References found in this work BETA

Probability and the Logic of Rational Belief.Henry Ely Kyburg - 1961 - Middletown, Conn., Wesleyan University Press.
The Paradox of the Preface.David C. Makinson - 1965 - Analysis 25 (6):205.

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Citations of this work BETA

Demystifying Dilation.Arthur Paul Pedersen & Gregory Wheeler - 2014 - Erkenntnis 79 (6):1305-1342.
Conditionals and Consequences.Gregory Wheeler, Henry E. Kyburg & Choh Man Teng - 2007 - Journal of Applied Logic 5 (4):638-650.
Applied Logic Without Psychologism.Gregory Wheeler - 2008 - Studia Logica 88 (1):137-156.

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