Term graphs and the NP-completeness of the product-free Lambek calculus

Abstract

We provide a graphical representation of proofs in the product-free Lambek calculus, called term graphs, that is related to several other proof net presentations. The advantage of term graphs is that they are very simple compared to the others. We use this advantage to provide an NP-completeness proof of the product-free Lambek Calculus that uses the reduction of [1]. Our proof is more intuitive due to the fact that term graphs allow arguments that are graphical in nature rather than using the algebraic arguments of [1]. © 2011 Springer-Verlag.