Properness and Consistency of Syntactico-Semantic Reasoning using PCFG and MEBN

Abstract

The paper proposes a formal approach for parsing grammatical derivations in the context of the principle of semantic compositionality by defining a mapping between Probabilistic Context Free Grammar (PCFG) and Multi Entity Bayesian Network (MEBN) theory, which is a first-order logic for modelling probabilistic knowledge bases. The principle of semantic compositionality states that meaning of compound expressions is dependent on meanings of constituent expressions forming the compound expression. Typical pattern analysis applications focus on syntactic patterns ignoring semantic patterns governing the domain in which pattern analysis is attempted. The paper introduces the concepts and terminologies of the mapping between PCFG and MEBN theory. Further the paper outlines a modified version of CYK parser algorithm for parsing PCFG derivations driven by MEBN. Using Kullback– Leibler divergence an outline for proving properness and consistency of the PCFG mapped with MEBN is discussed.