Browsing Mathematics by Author "Dautović, Šejla"
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Dautović, Šejla (Beograd , 2022)[more][less]
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 URI: http://hdl.handle.net/123456789/5452 Files in this item: 1
Doktorska_disertacija_sdautovic.pdf ( 1.181Mb )
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