Revision Rules for Convex Sets of Probabilities

Serafín Moral and Nic Wilson
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Serafín Moral: Universidad de Granada, Departamento de Ciencias de la Computacion
Nic Wilson: Queen Mary and Westfield College, Department of Computer Science

A chapter in Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, 1995, pp 113-127 from Springer

Abstract: Abstract The best understood and most highly developed theory of uncertainty is Bayesian probability. There is a large literature on its foundations and there are many different justifications of the theory; however, all of these assume that for any proposition a, the beliefs in a and ⌝a are strongly tied together. Without compelling justification, this assumption greatly restricts the type of information that can be satisfactorily represented, e.g., it makes it impossible to represent adequately partial information about an unknown chance distribution P such as 0.6 ≤ P(a) ≤ 0.8. The strict Bayesian requirement that an epistemic state be a single probability function seems unreasonable. A natural extension of the Bayesian theory is thus to allow sets of probability functions and to consider constraints and bounds on these, and to calculate supremum and infimum values of the probabilities of propositions (known as Upper and Lower Probabilities) given the constraints. Early work on this includes Boole1 and Good2 and early appearances in the Artificial Intelligence literature include Quinlan3 and Nilsson4.

Keywords: Inference Rule; Belief Revision; Belief State; Belief Function; Revision Procedure (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-1-4899-1424-8_7

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