Reward versus risk in uncertain inference: Theorems and simulations

Review of Symbolic Logic 5 (4):574-612 (2012)
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Abstract

Systems of logico-probabilistic reasoning characterize inference from conditional assertions that express high conditional probabilities. In this paper we investigate four prominent LP systems, the systems _O, P_, _Z_, and _QC_. These systems differ in the number of inferences they licence _. LP systems that license more inferences enjoy the possible reward of deriving more true and informative conclusions, but with this possible reward comes the risk of drawing more false or uninformative conclusions. In the first part of the paper, we present the four systems and extend each of them by theorems that allow one to compute almost-tight lower-probability-bounds for the conclusion of an inference, given lower-probability-bounds for its premises. In the second part of the paper, we investigate by means of computer simulations which of the four systems provides the best balance of reward versus risk. Our results suggest that system _Z_ offers the best balance.

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Author Profiles

Gerhard Schurz
Heinrich Heine University Düsseldorf
Paul D. Thorn
Heinrich Heine University Düsseldorf

References found in this work

Counterfactuals.David K. Lewis - 1973 - Malden, Mass.: Blackwell.
Logical foundations of probability.Rudolf Carnap - 1950 - Chicago]: Chicago University of Chicago Press.
Scientific reasoning: the Bayesian approach.Peter Urbach & Colin Howson - 1993 - Chicago: Open Court. Edited by Peter Urbach.
Counterfactuals.David Lewis - 1973 - Philosophy of Science 42 (3):341-344.

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