Probabilistic Logics for Reasoning about Decision Making under Uncertainty

We investigate probabilistic propositional logics as a way of expressing, and reasoning about decision making under uncertainty of a probabilistic type, with the goal of providing a deductive basis for various decision support problems. We introduce logics with language features for representing probability, utility, and independence, and provide an interpretation with a possible world semantics. We extract as axioms and inference rules the main properties that characterize the reasoning tailored to acting rationally in the decision making scenarios. The introduced calculus is complete for the type of reasoning performed by the corresponding graphical models. The thesis addresses the advantages and challenges of the use of probabilistic logic in modelling and reasoning about decision making under uncertainty. It provides a survey into probabilistic logics, the problem of complete axiomatization of conditional independence, as well as an overview of some of the most important approaches towards decision making under uncertaint