Description Logics are languages that can be used to organize knowledge and information about a topic of interest in a structured way, so that it can be understood and processed by automated reasoning systems. We can extend a Description Logic with different kinds of constructors, each contributing to the expressiveness of the language and the computational complexity of reasoning with it. If we were interested in structuring quantitative knowledge about healthcare and biological systems, we might want to state rules such as "the probability that a subject suffers from disease X given that they exhibit at least a symptom of type Y is between 30 and 50%" or add numerical attributes and say, for instance, that "if a region A contains X virus units according to a certain quantification method and B is a subregion of A, then B has contains Y < X virus units".

In his research, Filippo De Bortoli investigates the expressive power of Description Logics extended with quantitative constructors using model theory, which is a branch of mathematical logic that studies the interactions between theories stated in a formal language and structures that satisfy these theories. In this lecture, he is going to provide a high-level overview of the mathematical tools that are used to distinguish Description Logics from one another and to characterize their expressive power.