  Stochastic And-Or grammars (AOG) extend traditional stochastic grammars of
language to model other types of data such as images and events. In this paper
we propose a representation framework of stochastic AOGs that is agnostic to
the type of the data being modeled and thus unifies various domain-specific
AOGs. Many existing grammar formalisms and probabilistic models in natural
language processing, computer vision, and machine learning can be seen as
special cases of this framework. We also propose a domain-independent inference
algorithm of stochastic context-free AOGs and show its tractability under a
reasonable assumption. Furthermore, we provide two interpretations of
stochastic context-free AOGs as a subset of probabilistic logic, which connects
stochastic AOGs to the field of statistical relational learning and clarifies
their relation with a few existing statistical relational models.
