Inductive logic for rich languages

Jan-Willem Romeijn (Groningen) gives a talk at the MCMP Colloquium (19 December, 2013) titled "Inductive logic for rich languages". Abstract: I present an extension of the language of inductive logic with a formally precise notion of statistical hypothesis. I argue that this enhances the expressivity of inductive logic and provides an intuitive understanding of several Carnapian systems, e.g., systems that accommodate analogical predictions. The paper is set up as a guided tour passing a number of important sites: Carnapian inductive logic, De Finetti's representation theorem, Gaifman and Snir's often overlooked notion of rich language, von Mises Kollektivs, Bayesian statistical inference, the convergence theorems for it, and analogical predictions. All of these will be integrated into a single coherent story.