Using Tableaux to Automate the Lambek and Other Categorial Calculi

Abstract

We argue that, although labeled deduction can be quite costly in general, the complexity of keeping track of the label constraints built to encode the structure of the proofs does not necessarily render the strategy impractical. The point is illustrated with LLKE, a tableaux system for specification and test of categorial grammars. The paper presents and discusses the application of theorem proving in labeled analytic tableaux to natural language processing (NLP), describes algorithms and rules for tableau generation, introduces a new label-checking strategy, and identifies places where the complexity of the task can be tamed.