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Abstract:
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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 |