A Polynomial Time Algorithm for Parsing with the Bounded Order Lambek Calculus

Fowler (2008) introduced the bounded-order Lambek Calculus and provided a polynomial time algorithm for its sequent derivability. However, this result is limited because it requires exponential time in the presence of lexical ambiguity. That is, Fowler (2008) did not provide a polynomial time parsing algorithm. The purpose of this paper will be to provide such an algorithm. We will prove an asymptotic bound of O(n) for parsing and improve the bound for sequent derivability from O(n) to O(n).