Maps in multiple belief change

Peppas, P; Koutras, CD; Williams, MA

Maps in multiple belief change

Peppas, P

Koutras, CD Williams, MA

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Publication Type:: Journal Article
Citation:: ACM Transactions on Computational Logic, 2012, 13 (4)
Issue Date:: 2012-10-01

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Field	Value	Language
dc.contributor.author	Peppas, P https://orcid.org/0000-0002-0008-5505	en_US
dc.contributor.author	Koutras, CD	en_US
dc.contributor.author	Williams, MA https://orcid.org/0000-0002-1047-0503	en_US
dc.date.issued	2012-10-01	en_US
dc.identifier.citation	ACM Transactions on Computational Logic, 2012, 13 (4)	en_US
dc.identifier.issn	1529-3785	en_US
dc.identifier.uri	http://hdl.handle.net/10453/22850
dc.description.abstract	Multiple Belief Change extends the classical AGM framework for Belief Revision introduced by Alchourron, Gardenfors, and Makinson in the early '80s. The extended framework includes epistemic input represented as a (possibly infinite) set of sentences, as opposed to a single sentence assumed in the original framework. The transition from single to multiple epistemic input worked out well for the operation of belief revision. The AGM postulates and the system-of-spheres model were adequately generalized and so was the representation result connecting the two. In the case of belief contraction however, the transition was not as smooth. The generalized postulates for contraction, which were shown to correspond precisely to the generalized partial meet model, failed to match up to the generalized epistemic entrenchment model. The mismatch was fixed with the addition of an extra postulate, called the limit postulate, that relates contraction by multiple epistemic input to a series of contractions by single epistemic input. The new postulate however creates problems on other fronts. First, the limit postulate needs to be mapped into appropriate constraints in the partial meet model. Second, via the Levi and Harper Identities, the new postulate translates into an extra postulate for multiple revision, which in turn needs to be characterized in terms of systems of spheres. Both these open problems are addressed in this article. In addition, the limit postulate is compared with a similar condition in the literature, called (K*F), and is shown to be strictly weaker than it. An interesting aspect of our results is that they reveal a profound connection between rationality in multiple belief change and the notion of an elementary set of possible worlds (closely related to the notion of an elementary class of models from classical logic). © 2012 ACM.	en_US
dc.relation.ispartof	ACM Transactions on Computational Logic	en_US
dc.relation.isbasedon	10.1145/2362355.2362358	en_US
dc.subject.classification	Computation Theory & Mathematics	en_US
dc.title	Maps in multiple belief change	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	13	en_US
utslib.for	0802 Computation Theory and Mathematics	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	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 Computer Science
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	13	en_US

Abstract:

Multiple Belief Change extends the classical AGM framework for Belief Revision introduced by Alchourron, Gardenfors, and Makinson in the early '80s. The extended framework includes epistemic input represented as a (possibly infinite) set of sentences, as opposed to a single sentence assumed in the original framework. The transition from single to multiple epistemic input worked out well for the operation of belief revision. The AGM postulates and the system-of-spheres model were adequately generalized and so was the representation result connecting the two. In the case of belief contraction however, the transition was not as smooth. The generalized postulates for contraction, which were shown to correspond precisely to the generalized partial meet model, failed to match up to the generalized epistemic entrenchment model. The mismatch was fixed with the addition of an extra postulate, called the limit postulate, that relates contraction by multiple epistemic input to a series of contractions by single epistemic input. The new postulate however creates problems on other fronts. First, the limit postulate needs to be mapped into appropriate constraints in the partial meet model. Second, via the Levi and Harper Identities, the new postulate translates into an extra postulate for multiple revision, which in turn needs to be characterized in terms of systems of spheres. Both these open problems are addressed in this article. In addition, the limit postulate is compared with a similar condition in the literature, called (K*F), and is shown to be strictly weaker than it. An interesting aspect of our results is that they reveal a profound connection between rationality in multiple belief change and the notion of an elementary set of possible worlds (closely related to the notion of an elementary class of models from classical logic). © 2012 ACM.

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http://hdl.handle.net/10453/22850