Switch graphs for parsing type logical grammars

Abstract

Parsing in type logical grammars amounts to theorem proving in a substructural logic. This paper takes the proof net presentation of Lambek's associative calculus as a case study. It introduces switch graphs for online maintenance of the Danos-Regnier acyclicity condition on proof nets. Early detection of Danos-Regnier acyclicity violations supports early failure in shift-reduce parsers. Normalized switch graphs represent the combinatorial potential of a set of analyses derived from lexical and structural ambiguities. Packing these subanalyses and memoizing the results leads directly to a dynamic programming algorithm for Lambek grammars.