Bridging Jeffrey's rule, AGM revision and dempster conditioning in the theory of evidence

Ma, J; Liu, W; Dubois, D; Prade, H

Bridging Jeffrey's rule, AGM revision and dempster conditioning in the theory of evidence

Ma, J Liu, W Dubois, D Prade, H

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Publication Type:: Journal Article
Citation:: International Journal on Artificial Intelligence Tools, 2011, 20 (4), pp. 691 - 720
Issue Date:: 2011-08-01

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Field	Value	Language
dc.contributor.author	Ma, J	en_US
dc.contributor.author	Liu, W	en_US
dc.contributor.author	Dubois, D	en_US
dc.contributor.author	Prade, H https://orcid.org/0000-0003-4586-8527	en_US
dc.date.issued	2011-08-01	en_US
dc.identifier.citation	International Journal on Artificial Intelligence Tools, 2011, 20 (4), pp. 691 - 720	en_US
dc.identifier.issn	0218-2130	en_US
dc.identifier.uri	http://hdl.handle.net/10453/32434
dc.description.abstract	Belief revision characterizes the process of revising an agent's beliefs when receiving new evidence. In the field of artificial intelligence, revision strategies have been extensively studied in the context of logic-based formalisms and probability kinematics. However, so far there is not much literature on this topic in evidence theory. In contrast, combination rules proposed so far in the theory of evidence, especially Dempster rule, are symmetric. They rely on a basic assumption, that is, pieces of evidence being combined are considered to be on a par, i.e. play the same role. When one source of evidence is less reliable than another, it is possible to discount it and then a symmetric combination operation is still used. In the case of revision, the idea is to let prior knowledge of an agent be altered by some input information. The change problem is thus intrinsically asymmetric. Assuming the input information is reliable, it should be retained whilst the prior information should be changed minimally to that effect. To deal with this issue, this paper defines the notion of revision for the theory of evidence in such a way as to bring together probabilistic and logical views. Several revision rules previously proposed are reviewed and we advocate one of them as better corresponding to the idea of revision. It is extended to cope with inconsistency between prior and input information. It reduces to Dempster rule of combination, just like revision in the sense of Alchourrón, Gärdenfors, and Makinson (AGM) reduces to expansion, when the input is strongly consistent with the prior belief function. Properties of this revision rule are also investigated and it is shown to generalize Jeffrey's rule of updating, Dempster rule of conditioning and a form of AGM revision. © 2011 World Scientific Publishing Company.	en_US
dc.relation.ispartof	International Journal on Artificial Intelligence Tools	en_US
dc.relation.isbasedon	10.1142/S0218213011000401	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	Bridging Jeffrey's rule, AGM revision and dempster conditioning in the theory of evidence	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	20	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
utslib.for	1702 Cognitive Sciences	en_US
utslib.for	0802 Computation Theory and Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Software
pubs.organisational-group	/University of Technology Sydney/Strength - CAI - Centre for Artificial Intelligence
utslib.copyright.status	closed_access
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	20	en_US

Abstract:

Belief revision characterizes the process of revising an agent's beliefs when receiving new evidence. In the field of artificial intelligence, revision strategies have been extensively studied in the context of logic-based formalisms and probability kinematics. However, so far there is not much literature on this topic in evidence theory. In contrast, combination rules proposed so far in the theory of evidence, especially Dempster rule, are symmetric. They rely on a basic assumption, that is, pieces of evidence being combined are considered to be on a par, i.e. play the same role. When one source of evidence is less reliable than another, it is possible to discount it and then a symmetric combination operation is still used. In the case of revision, the idea is to let prior knowledge of an agent be altered by some input information. The change problem is thus intrinsically asymmetric. Assuming the input information is reliable, it should be retained whilst the prior information should be changed minimally to that effect. To deal with this issue, this paper defines the notion of revision for the theory of evidence in such a way as to bring together probabilistic and logical views. Several revision rules previously proposed are reviewed and we advocate one of them as better corresponding to the idea of revision. It is extended to cope with inconsistency between prior and input information. It reduces to Dempster rule of combination, just like revision in the sense of Alchourrón, Gärdenfors, and Makinson (AGM) reduces to expansion, when the input is strongly consistent with the prior belief function. Properties of this revision rule are also investigated and it is shown to generalize Jeffrey's rule of updating, Dempster rule of conditioning and a form of AGM revision. © 2011 World Scientific Publishing Company.

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http://hdl.handle.net/10453/32434