Parsing PCFG within a General probabilistic inference framework

Abstract

One of the aims of Artificial General Intelligence(AGI) is to use the same methods to reason over a large number of problems spanning different domains. Therefore, advancing general tools that are used in a number of domains like language, vision and intention reading is a step toward AGI. Probabilistic Context Free Grammar (PCFG) is one such formalism used in many domains. However, many of these problems can be dealt with more effectively if relationships beyond those encoded in PCFGs (category, order and parthood) can be included in inference. One obstacle to using more general inference approaches for PCFG parsing is that these approaches often require all state variables in a' domain to be known in advance. However, since some PCFGs license infinite derivations, it is in general impossible to know all state variables before inference. Here, we show how to express PCFGs in a new probabilistic framework that enables inference over unknown objects. This approach enables joint reasoning over both constraints encoded by a PCFG and other constraints relevant to a problem. These constraints can be encoded in a first-order language that in addition to encoding causal conditional probabilities can also represent (potentially cyclic) boolean constraints.