The generative capacity of the Lambek-Grishin calculus: A new lower bound

Abstract

The Lambek-Grishin calculus LG is a categorial type logic obtained by adding a family of connectives {⊕, ∅, unknown sign} dual to the family {⊗, /, \}, and adding interaction postulates between the two families of connectives thus obtained. In this paper, we prove a new lower bound on the generative capacity of LG, namely the class of languages that are the intersection of a context-free language and the permutation closure of a context-free language. This implies that LG recognizes languages like the MIX language, e.g. the permutation closure of {anbnc n | n ∈ IN}, and {anbncnd nen | n ∈ IN}, which can not be recognized by tree adjoining grammars. © 2011 Springer-Verlag.