Inference with Relational Theories over Infinite Domains

Many important tasks can be cast as weighted relational satisfiability problems. Propositionalizing relational theories and making inferences with them using SAT algorithms has proven effective in many cases. However, these approaches require that all objects in a domain be known in advance. Many domains, from language understanding to machine vision, involve reasoning about objects that are not known beforehand. Theories with unknown objects can require models with infinite objects in their domain and thus lead to propositionalized SAT theories that existing algorithms cannot deal with. To address these problems, we characterize a class of relational generative weighted satisfiability theories (GenSAT) over potentially infinite domains and propose an algorithm, GenDPLL, for finding models of these theories. We introduce the notion of a relevant model and an increasing cost theory to identify conditions under which GenDPLL is complete, even when a theory has infinite models.