Thesis (PhD (Mathematics))--University of Stellenbosch, 2010. / 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/5353 |
| Date | 12 1900 |
| Creators | Jeftha, Lindsey Craig |
| Contributors | Rewitzky, Ingrid, University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 86 p. |
| Rights | University of Stellenbosch |
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