Logical relations in a statistical problem
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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In Benedikt Lowe, Jan-Willem Romeijn & Eric Pacuit (eds.), Proceedings of the Foundations of the Formal Sciences VI: Reasoning about probabilities and probabilistic reasoning. College Publications (2008)
This paper presents the progicnet programme. It proposes a general framework for probabilistic logic that can guide inference based on both logical and probabilistic input. After an introduction to the framework as such, it is illustrated by means of a toy example from psychometrics. It is shown that the framework can accommodate a number of approaches to probabilistic reasoning: Bayesian statistical inference, evidential probability, probabilistic argumentation, and objective Bayesianism. The framework thus provides insight into the relations between these approaches, it illustrates how the results of different approaches can be combined, and it provides a basis for doing efficient inference in each of the approaches.
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