Towards efficient parsing with proof-nets

Abstract

This paper presents a method for parsing associative Lambek grammars based on graph-theoretic properties. Connection graphs, which are a simplified version of proof-nets, are actually a mere conservative extension of the earlier method of syntactic connexion, discovered by Ajduckiewicz [1935]. The method amounts to find alternating spanning trees in graphs. A sketch of an algorithm for finding such a tree is provided. Interesting properties of time-complexity for this method are expected. It has some similarities with chart-parsing ([König. 1991, 1992], [Hepple, 1992]) but is different at least in the fact that intervals are here edges and words are vertices (or trees) instead of the contrary in classical chart-parsing.