A model theoretic approach to relational learning in artificial intelligence

Statistical Relational Artifical Intelligence (SRAI) is a branch of AI which combines the logical and the statistical schools of AI.

The concepts developed in SRAI, such as (parametrized) probabilistic graphical models (PGMs), are quite powerful in theory.

But a crucial obstacle to their wider use in applications is that scalable algorithms (i.e. "fast on large inputs") for learning a PGM and/or using it for making inferences are generally lacking.

This project addresses this issue by using methodology from (finite) model theory to study probability distributions on spaces of finite structures (representing possible states of the world) that are determined by PGMs.

Different formal logics play a role since such are used to define queries/events and/or to define (conditional) probabilities in PGMs.

We are in particular interested in the phenomena of "logical convergence laws" and "asymptotic elimination of aggregators" (e.g. quantifiers), since when these phenomena occur they tend to imply that there are scalable algorithms of learning and inference.

By using the concept of "inference framework" one can compare and classify different combinations (G, L) of a PGM G and a logic L with respect to their expressive strength on large domains of objects. The expressive strength of an inference framework is related to the existence of scalable algorithms for it.