Pregroup Grammars, their Syntax and Semantics
This work tackles a foundational ambiguity problem in algebraic grammar models, which is incremental as it builds on Lambek's prior suggestions without presenting new empirical results.
The paper addresses the ambiguity problem in the set-theoretic semantics of pregroup grammars by exploring whether composition should use direct sum or tensor product of finite-dimensional vector spaces, as suggested by Lambek to potentially resolve this issue.
Pregroup grammars were developed in 1999 and stayed Lambek's preferred algebraic model of grammar. The set-theoretic semantics of pregroups, however, faces an ambiguity problem. In his latest book, Lambek suggests that this problem might be overcome using finite dimensional vector spaces rather than sets. What is the right notion of composition in this setting, direct sum or tensor product of spaces?