Generative Modeling with Failure in PRISM

PRISM is a logic-based Turing-complete symbolic-statistical modeling language with a built-in parameter learning routine. In this paper, we enhance the modeling power of PRISM by allowing general PRISM programs to fail in the generation process of observable events. Introducing failure extends the class of definable distributions but needs a generalization of the semantics of PRISM programs. We propose a three valued probabilistic semantics and show how failure enables us to pursue constraint-based modeling of complex statistical phenomena.