In this talk, we will introduce the basic tools and terminology for future talks on Machine Learning and Statistical Applications. Fitting with the theme of this seminar, we will also touch on concepts regarding the physical meaning of "information" and its connections with Statistics.
I shall introduce and describe the subject of modal model theory, in which one studies a mathematical structure within a class of similar structures under an extension concept, giving rise to mathematically natural notions of possibility and necessity, a form of mathematical potentialism. We study the class of all graphs, or all groups, all fields, all orders, or what have you; a natural case is the class of all models of a fixed first-order theory. In this talk, I shall describe some of the resulting elementary theory, particularly the remarkable expressive power of modal graph theory. This is joint work with my Oxford student Wojciech Woloszyn.
Statistics and Mathematical Physics