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On the Logic of Theory Change: Relations between Incision and Selection Functions
2006 (English)In: ECAI 2006, PROCEEDINGS, 2006, Vol. 141, 402-406 p.Conference paper, Published paper (Refereed)
Abstract [en]

This work elaborates on the connection between partial meet contractions and kernel contractions in belief change theory. We present a way to define incision functions (used in kernel contractions) from selection functions (used in partial meet contractions) and vice versa. Then we make precise under which conditions there are exact correspondences between selection and incision functions so that the same contraction operations can be obtained by using either of them.

Place, publisher, year, edition, pages
2006. Vol. 141, 402-406 p.
Series
Frontiers in Artificial Intelligence and Applications, ISSN 0922-6389
Keyword [en]
Belief Revision, AGM Theory, Partial Meet Contractions, Kernel Contractions
National Category
Computer Engineering
Identifiers
URN: urn:nbn:se:kth:diva-29594ISI: 000273875100078ISBN: 978-1-58603-642-3 (print)OAI: oai:DiVA.org:kth-29594DiVA: diva2:396571
Conference
17th European Conference on Artificial Intelligence Riva del Garda, ITALY, AUG 28, 2006
Note
QC 20110210Available from: 2011-02-10 Created: 2011-02-10 Last updated: 2011-02-11Bibliographically approved
In thesis
1. On the Logic of Theory Change: Extending the AGM Model
Open this publication in new window or tab >>On the Logic of Theory Change: Extending the AGM Model
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists in six articles and a comprehensive summary.

• The pourpose of the summary is to introduce the AGM theory of belief change and to exemplify the diversity and significance of the research that has been inspired by the AGM article in the last 25 years. The research areas associated with AGM was divided in three parts: criticisms, where we discussed some of the more common criticisms of AGM. Extensions where the most common extensions and variations of AGM are presented and applications where we provided an overview of applications and connections with other areas of research.

• Article I elaborates on the connection between partial meet contractions [AGM85] and kernel contractions [Han94a] in belief change theory. Also both functions are equivalent in belief sets, there are notequivalent in belief bases. A way to define incision functions (used in kernel contractions) from selection functions (used in partial meet contractions) and vice versa is presented. It is explained under which conditions there are exact correspondences between selection and incision functions so that the same contraction operations can be obtained by using either of them.

• Article II proposes an axiomatic characterization for ensconcement-based contraction functions, belief base functions proposed byWilliams and relates this function with other kinds of base contraction functions.

• Article III adapts the Fermé and Hansson model of Shielded Contraction [FH01] as well as Hansson et all Credibility-Limited Revision [HFCF01] for belief bases, to join two of the many variations of the AGM model [AGM85], i.e. those in which knowledge is represented through belief bases instead of logic theories, and those in which the object of the epistemic change does not get the priority over the existing information as it is the case in the AGM model.

• Article IV introduces revision by comparison a refined method for changing beliefs by specifying constraints on the relative plausibility of propositions. Like the earlier belief revision models, the method proposed is a qualitative one, in the sense that no numbers are needed in order to specify the posterior plausibility of the new information. The method uses reference beliefs in order to determine the degree of entrenchment of the newly accepted piece of information. Two kinds of semantics for this idea are proposed and a logical characterization of the new model is given.

• Article V focuses on the extension of AGM that allows change for a belief base by a set of sentences instead of a single sentence. In [FH94], Fuhrmann and Hansson presented an axiomatic for Multiple Contraction and a construction based on the AGM Partial Meet Contraction. This essay proposes for their model another way to construct functions: Multiple Kernel Contraction, that is a modification of Kernel Contraction,proposed by Hansson [Han94a] to construct classical AGM contractions and belief base contractions.

• Article VI relates AGM model with the DFT model proposed by Carlos Alchourrón [Alc93]. Alchourrón devoted his last years to the analysis of the notion of defeasible conditionalization. His definition of the defeasible conditional is given in terms of strict implication operator and a modal operator f which is interpreted as a revision function at the language level. This essay points out that this underlying revision function is more general than AGM revision. In addition, a complete characterization of that more general kind of revision that permits to unify models of revision given by other authors is given.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. x, 51 p.
Keyword
Logic of Theory Change. AGM model. Belief Bases, Iterated Models, Multiple belief change, AGM and defeasible Logic
National Category
Philosophy
Identifiers
urn:nbn:se:kth:diva-29601 (URN)
Public defence
2011-02-21, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20110211Available from: 2011-02-11 Created: 2011-02-10 Last updated: 2011-02-11Bibliographically approved

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Citation style
  • apa
  • harvard1
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