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Belief Change Rules in Ordinal and Numerical Uncertainty Theories

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Belief Change

Part of the book series: Handbook of Defeasible Reasoning and Uncertainty Management Systems ((HAND,volume 3))

Abstract

The situation of belief change in numerical uncertainty frameworks differs from the situation in classical logic in two respects: on the one hand, uncertainty theories are tailored to representing epistemic states involving shades of belief and are more expressive than classical logic in that respect. Indeed, considering a propositional belief set (a set of accepted beliefs) from the standpoint of uncertainty, a proposition is only surely true (it belongs to the belief set), surely false (its negation belongs to the belief set) or unknown (neither the proposition nor its negation belong to the belief set). Uncertainty theories express the extent to which an ultimately true or false proposition is believed. On the other hand, many logical-oriented belief revision theories are syntax-dependent (e.g., [Nebel, 1992], and in this book)—although they are semantically meaningful—while uncertainty theories adopt a semantic representation of epistemic states. In syntax-dependent theories of revision two logically equivalent, syntactically distinct, belief bases are generally not revised in the same way. The syntactic dimension of logical approaches introduces a level of increased complexity and expressiveness that cannot be grasped in the usual uncertainty theories. So, uncertainty theories are altogether more refined and less expressive than logical syntax-dependent approaches for the purpose of belief change.

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Authors and Affiliations

  1. Institut de Recherche en Informatique de Toulouse (IRIT), Toulouse, France

    Didier Dubois & Henri Prade

  2. Department of Computer Science and Artificial Intelligence (DECSAI), University of Granada, Spain

    Serafin Moral

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  1. Didier Dubois
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  2. Serafin Moral
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  1. Université Paul Sabatier, Toulouse, France

    Didier Dubois  & Henri Prade  & 

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Dubois, D., Moral, S., Prade, H. (1998). Belief Change Rules in Ordinal and Numerical Uncertainty Theories. In: Dubois, D., Prade, H. (eds) Belief Change. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5054-5_8

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