Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
What does a conditional knowledge base entail?
Artificial Intelligence
General patterns in nonmonotonic reasoning
Handbook of logic in artificial intelligence and logic programming (vol. 3)
Reasoning about Uncertainty
Reasoning About Knowledge
System Z: a natural ordering of defaults with tractable applications to nonmonotonic reasoning
TARK '90 Proceedings of the 3rd conference on Theoretical aspects of reasoning about knowledge
Rational Acceptance and Conjunctive/Disjunctive Absorption
Journal of Logic, Language and Information
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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 nonmonotonic 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 ∨.