Logics with Probability Operators

Logic and Computation Courses

Advanced Course

Logics with Probability Operators,
Zoran Ognjanovic (Serbian Academy of Sciences and Arts, Serbia) and Dragan Doder (University of Belgrade, Serbia)

Formal reasoning with uncertain knowledge is an ancient problem dating, at least, from Leibniz. Recently we are experiencing a growing interest in the field motivated by applications to computer science and artificial intelligence. Some of the formalisms for representing, and reasoning with, uncertain knowledge are based on probabilistic logics, that extend classical logic calculus with probabilistic operators.

The main goal of this course is to provide a solid foundation for students that want to use results and ideas from probability logics in their field of study. We will present mathematical techniques, including the results of the authors, in a number of probabilistic logics. We will consider various propositional and first-order languages with probabilistic operators, with different expressive power and different co-domains of probability measures. For all those logics we will present existing axiomatization approaches, and we will discuss decidability issues. We will also consider how to extend the approaches for probabilistic languages thatextend different modal logics.

The course will provide a thorough introduction to the field of probability logics, with basic prerequisites (familiarity with modal logic and probability theory). It will include many technical details, and in consequence it is intended for an advanced audience.