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Extending the Harper Identity to Iterated Belief Change [article]

Jake Chandler, Richard Booth
2016 arXiv   pre-print
In this paper we extend the Harper Identity from single-step change to define iterated contraction in terms of iterated revision.  ...  Specifically, just as the Harper Identity provides a recipe for defining the belief set resulting from contracting A in terms of (i) the initial belief set and (ii) the belief set resulting from revision  ...  Conclusions We have shown that the issue of extending the Harper identity to iterated belief change (a) is not a straightforward affair but (b) can be fruitfully approached by combining a pair of total  ... 
arXiv:1604.05419v1 fatcat:yv3n35lm5jcltlcyfhfv7u4l7q

Minimal belief change, Pareto-optimality and logical consequence

Oliver Schulte
2002 Economic Theory  
Once we have iterated belief change in view, it is natural to ask what the long-run behaviour of methods for iterated belief change is.  ...  The Content of the Levi and Harper Identities The Levi Identity stipulates a constraint on revision functions for minimal belief change by connecting them to belief contraction.  ...  Extending the previous notation, I write T ¤p for the result of applying a belief revision function ¤ to a theory T and a formula p.  ... 
doi:10.1007/s001990100194 fatcat:vk3vt6it7fdbfaob46duf33ixe

Rational Defeasible Belief Change

Giovanni Casini, Thomas Meyer, Ivan Varzinczak
2020 Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning  
The investigation leads us to the consideration of the problem of iterated change, generalising the classical work of Darwiche and Pearl.  ...  In this paper we consider the classical AGM belief change operators, contraction and revision, applied to a defeasible setting in the style of Kraus, Lehmann, and Magidor.  ...  It turns out that an extension to iterated belief change in the style of Darwiche and Pearl (1997) addresses this deficiency.  ... 
doi:10.24963/kr.2020/22 dblp:conf/kr/CasiniMV20 fatcat:gj7sruxl7jbvrm2pwftpeaww4u

Basic Infobase Change [chapter]

Thomas Meyer
1999 Lecture Notes in Computer Science  
In one view, a base should be thought of as providing more structure to its generated belief set, and can be used to determine the theory change operation associated with a base change operation.  ...  The associated theory change operations satisfy the AGM postulates for theory change [1] . Since an infobase change operation produces a new infobase, it allows for iterated infobase change.  ...  We have extended the initial infobase proposal of Meyer et al. [12] , but much still needs to be done.  ... 
doi:10.1007/3-540-46695-9_14 fatcat:7lpa2h43kzdfzkltfcb365rq2i

A Conditional Perspective for Iterated Belief Contraction [article]

Kai Sauerwald and Gabriele Kern-Isberner and Christoph Beierle
2019 arXiv   pre-print
This is especially because for iterated belief change the connection between revision and contraction via the Levi and Harper identity is not straightforward, and therefore, characterisation results do  ...  According to Boutillier, Darwiche, Pearl and others, principles for iterated revision can be characterised in terms of changing beliefs about conditionals.  ...  and contraction via the Levi and Harper identities [13, 17] .  ... 
arXiv:1911.08833v1 fatcat:s2bv3eeaavgxzmlgyy6fn7pamq

A Consistency-Based Model for Belief Change: Preliminary Report [article]

James Delgrande, Torsten Schaub
2000 arXiv   pre-print
We present a general, consistency-based framework for belief change. Informally, in revising K by A, we begin with A and incorporate as much of K as consistently possible.  ...  Our framework differs from work based on ordinal conditional functions, notably with respect to iterated revision.  ...  As well, it supports iterated revision. Finally, the framework is applicable to other approaches to belief change.  ... 
arXiv:cs/0003052v3 fatcat:nvaukn5jlrekvida7hcy7jdoxe

Dynamic Preference Logic meets Iterated Belief Change: Representation Results and Postulates Characterization

Marlo Souza, Renata Vieira, Álvaro Moreira
2020 Theoretical Computer Science  
This work investigates how Dynamic Preference Logic, a logic in the DEL family, can be used to study properties of dynamic belief change operators, focusing on well-known postulates of iterated belief  ...  AGM's belief revision is one of the main paradigms in the study of belief change operations.  ...  and Harper identities [1] .  ... 
doi:10.1016/j.tcs.2020.12.042 fatcat:53lyxtxeejdizbrgsi6qketcy4

Belief Revision, Conditional Logic and Nonmonotonic Reasoning

Wayne Wobcke
1995 Notre Dame Journal of Formal Logic  
This is first generalized to allow the iteration of theory change operations to capture the dynamics of epistemic states according to a principle of minimal change of entrenchment.  ...  of beliefs and hence the weakened scope of our extended postulates.  ...  the theory change algorithms and on the implementation of the belief revision system.  ... 
doi:10.1305/ndjfl/1040308829 dblp:journals/ndjfl/Wobcke95 fatcat:weqac4q675anplea7lym2fxz4u

Dynamics of Beliefs [chapter]

Sébastien Konieczny
2011 Lecture Notes in Computer Science  
The dynamics of beliefs is one of the major components of any autonomous system, that should be able to incorporate new pieces of information.  ...  In this paper we give a quick overview of the main operators for belief change, in particular revision, update, and merging, when the beliefs are represented in propositional logic.  ...  operator can be used to define a contraction operator through the Harper identity [2, 35] .  ... 
doi:10.1007/978-3-642-23963-2_6 fatcat:hixovxyrx5fehi5rack2vko5ja

Probability, coherent belief and coherent belief changes

John Cantwell, Hans Rott
2019 Annals of Mathematics and Artificial Intelligence  
We show that it fails to satisfy the traditional principles of Inclusion and Preservation for belief revision and the principle of Recovery for belief withdrawals, as well as the Levi and Harper identities  ...  We take this to be a problem for the latter principles rather than for the idea of coherent belief change.  ...  , and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s10472-019-09649-3 fatcat:nfabuilik5fgfmklgclkix3lvu

AGM, Ranking Theory, and the Many Ways to Cope with Examples [chapter]

Wolfgang Spohn
2013 David Makinson on Classical Methods for Non-Classical Problems  
The paper first explains how the ranking-theoretic belief change or conditionalization rules entail all of the standard AGM belief revision and contraction axioms.  ...  And the other conclusion will be that because of those complexities any inference from such examples to the shape of the basic principles of belief change is premature and problematic.  ...  As to the relation between AGM revision and contraction, I should add that the Levi Identity and the Harper Identity also hold according to the ranking-theoretic account of those operations: The Levi Identity  ... 
doi:10.1007/978-94-007-7759-0_6 fatcat:jndprl77rngbzdu262h52ci4mi

Credible Information, Allowable Information and Belief Revision - Extended Abstract

Giacomo Bonanno
2019 Electronic Proceedings in Theoretical Computer Science  
In this paper we extend the re-interpretation of (a generalized notion of) choice structure in terms of belief revision by adding: (1) the possibility that an item of "information" might be discarded as  ...  ) and the syntactic belief revision functions of the AGM theory (developed in philosophy and computer science).  ...  AGM7 and AGM8 are a generalization of AGM3 and AGM4 that "applies to iterated changes of belief.  ... 
doi:10.4204/eptcs.297.6 fatcat:i7gfi4qjhrdgzc7ueh3w46bjzu

AGM Contraction and Revision of Rules

Guido Boella, Gabriella Pigozzi, Leendert van der Torre
2016 Journal of Logic, Language and Information  
The results in this paper suggest that, in general, results from belief base dynamics can be transferred to rule base dynamics, but that a similar transfer of AGM theory change to rule change is much more  ...  First, we generalise belief base contraction to rule base contraction, and show that two representation results of Hansson still hold for rule base contraction.  ...  Acknowledgments Thanks to David Makinson and Jörg Hansen for discussions on the issues raised in this paper.  ... 
doi:10.1007/s10849-016-9244-9 fatcat:tbxxgvwb7zfv3fobmldpboaa7u

A consistency-based approach for belief change

James P Delgrande, Torsten Schaub
2003 Artificial Intelligence  
The approach is wellsuited for implementation: belief change can be equivalently expressed in terms of a finite knowledge base; and the scope of a belief change operation can be restricted to just those  ...  propositions common to the knowledge base and sentence for change.  ...  (As Section 4.3 shows, one cannot just use the Harper Identity to obtain these latter operations.)  ... 
doi:10.1016/s0004-3702(03)00111-5 fatcat:cmc4jg4xqrfljarj3tqtlhawu4

Hypothetical revision and matter-of-fact supposition [article]

Horacio Arlo-Costa
2000 arXiv   pre-print
The notion of qualitative change of view that thus arises is axiomatized and compared with standard notions like AGM and UPDATE.  ...  The paper studies the notion of supposition encoded in non-Archimedean conditional probability (and revealed in the acceptance of the so-called indicative conditionals).  ...  I would like to thank as well two anonymous referees for their helpful comments.  ... 
arXiv:cs/0003022v1 fatcat:6pcq6ntzwrgenijeu4qahrawdi
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