LOGIČKO MODELOVANJE BAJESIJANSKE TEORIJE POTVRĐIVANJA

eBibliothek Repositorium

 
 

LOGIČKO MODELOVANJE BAJESIJANSKE TEORIJE POTVRĐIVANJA

Zur Kurzanzeige

dc.contributor.advisor Ikodinović, Nebojša
dc.contributor.author Dautović, Šejla
dc.date.accessioned 2022-09-08T13:52:05Z
dc.date.available 2022-09-08T13:52:05Z
dc.date.issued 2022
dc.identifier.uri http://hdl.handle.net/123456789/5452
dc.description.abstract The goal of this dissertation is to develop logics with the aim of formalizing Bayesian confirmation theory. As such, the very topic of this dissertation is in the field of probabilistic logic. In Bayesian theory there are qualitative and quantitative concepts of confirmation. Ac- cording to the first of these two terms, the event E probabilistically confirms the second event F if the conditional probability of the event F (with the condition E) is greater than unconditional probabilities. On the other hand, the quantitative approach studies the degree to which E confirms F , which is formalized by relevance measures of confirmation, binary functions with arguments E and F . Carnap used the notion of the degree of confirmation as the basic term for the formal apparatus of inductive logic. The main results of the dissertation are probabilistic logics with operators of confirma- tion that correspond to existing measures of relevance from the literature, and theoretical predictions related to these logics, such as deduction and completeness theorems, as well as decision results. The importance of the development of such logical systems, except in the direct formalization of important Bayesian concepts, lies in their expressiveness: for each measure of relevance that will be logically formalized, the resulting logical language is rich enough to express many basic operators of probabilistic logic from the literature, which are the operators of standard probability, qualitative confirmation and independence. The com- pleteness of these logical systems is proven in relation to the standard class of measurable models, which consist of Kripke’s structures in which the accessibility relation is replaced by a probabilistic measure defined over all possible worlds. The second part of the dissertation is about dynamic aspect of confirmation in the sense that we monitor how much the realization of an event affects the realization of another event in the future. Accordingly, in this dissertation we constructed a branching-time temporal logic with ac- tions and probabilistic confirmation operators. The results of the first part were successfully modified to obtain the completeness result of this logic en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2022-09-08T13:52:05Z No. of bitstreams: 1 Doktorska_disertacija_sdautovic.pdf: 1181669 bytes, checksum: b0356d593fd8c1148767d464113e54af (MD5) en
dc.description.provenance Made available in DSpace on 2022-09-08T13:52:05Z (GMT). No. of bitstreams: 1 Doktorska_disertacija_sdautovic.pdf: 1181669 bytes, checksum: b0356d593fd8c1148767d464113e54af (MD5) Previous issue date: 2022 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title LOGIČKO MODELOVANJE BAJESIJANSKE TEORIJE POTVRĐIVANJA en_US
mf.author.birth-date 1992-05-12
mf.author.birth-place Novi Pazar en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srpkinja en_US
mf.subject.area Mathematics en_US
mf.subject.keywords Probabilistic logic, Temporal logic, Decidability, Completeness, Degree of con- firmation, Infinitary axiomatization. en_US
mf.subject.subarea Mathematical Logic en_US
mf.contributor.committee Doder, Dragan
mf.contributor.committee Janičić, Predrag
mf.contributor.committee Ognjanović, Zoran
mf.contributor.committee Moconja, Slavko
mf.university.faculty Mathematical faculty en_US
mf.document.references 69 en_US
mf.document.pages 84 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.university Belgrade University en_US

Dateien zu dieser Ressource

Dateien Größe Format Anzeige
Doktorska_disertacija_sdautovic.pdf 1.181Mb PDF Öffnen

Das Dokument erscheint in:

Zur Kurzanzeige