Grammars, Deductive Systems, and Parsing

Many theories of grammar and styles of grammar speciication have stemmed from mathematical logic, computer science, and computational linguistics, and have been used for describing natural languages. By a series of constructions, we relate categorial, attribute and logic grammars via (axiomatic) labelled deductive systems, and extend this relation to accommodate uniication-based grammars and so-called Montague Grammar. The axioms of a labelled deductive system can also be used to constrain the proof search by automatically generating an LR parser from them; we describe the implementation of such a parser-generator. Furthermore, we show how a modiication of the LR parsing algorithm, plus the (meta-level) information contained in the axioms, can be used to parse a grammar speciication which is based on procedural rather than combinatorial properties of the language.