An Earley-style Predictive Chart Parsing Method for Lambek Grammars

We present a new chart parsing method for Lambek grammars, inspired by a method for DTree grammar parsing. The formulae of a Lambek sequent are firstly converted into rules of an indexed grammar formalism, which are used in an Earley-style predictive chart algorithm. The method is non-polynomial, but performs well for practical purposes much better than previous chart methods for Lambek grammars. 1 I n t r o d u c t i o n We present a new chart parsing method for Lambek grammars. The starting point for this work is the observation, in (Hepple, 1998), of certain similarities between categorial grammars and the D-Tree grammar (DTG) formalism of Rambow et al. (1995a). On this basis, we have explored adapting the DTG parsing approach of Rambow et al. (1995b) for use with the Lambek calculus. The resulting method is one in which the formulae of a Lambek sequent that is to be proven are first converted to produce rules of a formalism which combines ideas from the multiset-valued linear indexed grammar formalism of Rainbow (1994), with the Lambek calculus span labelling scheme of Morrill (1995), and with the first-order compilation method for categorial parsing of Hepple (1996). The resulting 'grammar' is then parsed using an Earley-style predictive chart algorithm which is adapted from Rambow et al. (1995b). 2 T h e L a m b e k C a l c u l u s We are concerned with the implicational (or 'product-free') fragment of the associative Lambek calculus (Lambek, 1958). A natural deduction formulation is provided by the following rules of elimination and introduction, which correspond to steps of functional application and abstraction, respectively (as the term labelling reveals). The rules are sensitive to the order of assumptions. In the [/I] (resp. [\I]) rule, [B] indicates a discharged or withdrawn assumption, which is required to be the rightmost (resp. leftmost) of the proof. A / B :a B :b /E B : b B \ A a