Satisfiability and Model Counting in Open Universes

SAT and #SAT are at the heart of many important problem formulations in AI, the most prominent being reasoning and learning in first-order and probabilistic knowledge bases. In practice, all contemporary systems resort to domain closure: objects in the universe are all and only the ones mentioned in the knowledge base. This is in stark contrast to the natural ability of human beings to infer things about sensory inputs and unforeseen data: they infer the existence of objects from their observations; no predefined list of objects is given or known in advance. In this paper, we introduce the formal foundations for reasoning in open universes in a general way, purely based on SAT and #SAT technology.