Syntax-driven Analysis of Context-free Languages with Respect to Fuzzy Relational Semantics

A grammatical framework is presented that augments context-free production rules with semantic production rules that rely on fuzzy relations as representations of fuzzy natural language concepts. It is shown how the well-known technique of syntax-driven semantic analysis can be used to infer from an expression in a language defined in such a semantically augmented grammar a weak ordering on the possible worlds it describes. Considering the application of natural language query processing, we show how to order elements in the domain of a relational database scheme according to the degree to which they fulfill the intuition behind a given natural language statement like "Carol lives in a small city near San Francisco".