A topological framework for modeling belief revision

Jeftha, Lindsey Craig (Stellenbosch : University of Stellenbosch, 2010-12)

Thesis (PhD (Mathematics))--University of Stellenbosch, 2010.

Thesis

ENGLISH ABSTRACT: Classical formulations model belief revision as a deterministic process. Under certain circumstances, the process may have more than one outcome, which suggests that belief revision is non-deterministic instead. Representations exist that model belief revision in either format, and for both formats there are axiom schemes that determine whether the representation is in fact a belief revision process. Although the axiom scheme for the non-deterministic case generalises that of the deterministic case, both schemes entail that all of the beliefs held by an agent are affected by new information, which is perhaps unintuitive. Rather, one may consider that belief revision should be local, with beliefs only affected if the new information is pertinent to them. We approach the problem of belief revision from the standpoint that it is local and non-deterministic, and the purpose and contribution of this dissertation is the development of a topological framework with which to model belief revision in this manner.

AFRIKAANSE OPSOMMING: Geloofshersiening word gewoonlik as ’n deterministiese proses voorgestel. Meer as een uitkoms mag bestaan vir verskeie omstandighede, wat aandui dat die proses liewer nie-deterministies van aard is. Beide die gevalle word deur aksiomaskemas gereguleer, en die aksiomas vir die nie-deterministiese geval veralgemeen dié van die deterministiese geval. Albei aksiomaskemas stipuleer, miskien onintuïtief, dat alle gelowe van ’n agent deur die nuwe informasie geaffekteer word. ’n Beter metode is dat net daardie gelowe waarvoor die nuwe informasie toepaslik is geaffekteer word. Ons benader die probleem van geloofshersiening uit die standpunt dat dit lokaal en nie-deterministies is, en die doel en bydrae van hierdie proefskrif is dus die ontwikkeling van ’n topologiese raamwerk waarmee ons geloofshersiening op hierdie manier kan voorstel.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/5353
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