This site contains Lambek's recent papers, nearly all written in this millennium. They are mostly undated, so I have sorted them by subject matter, which mostly breaks up into linguistics, physics, and category theory. Most of the category theory was for the linguistics. Some of the papers are not complete, since I got them from his typist. Some were published (and I have provided the citations) and some are not. Among the unpublished, most are undated and a couple seem to be duplicates, doubtless revisions. If anyone figures out which the latest version is, I will try to remove the duplicates. If I was able to download the actual publication, it appears as a normal citation. If the citation is preceded by "Appeared in:", I was not able to download the actual publication, but I compiled and included the source file for what may not be the final version. Dates of writing or of appearance are provided when discernible. All in all it is a remarkable amount of writing for someone aged between 75 and 90. According to MathSciNet, he had 19 publications between 2001 and 2013.

A pregroup is a partially ordered monoid endowed with two unary operations called left and right adjunction. Pregroups were recently introduced to help with natural language processing, as we illustrate here by looking at small fragments of three modern European languages. As it turns out, the apparently new algebraic concept of a pregroup had been around for some time in recreational mathematics, although not under this name.

Grammar can be formulated as a kind of substructural propositional logic. In support of this claim, we survey bare Gentzen style deductive systems and two kinds
of non-commutative linear logic: intuitionistic and compact bilinear logic. We also glance at their categorical refinements

We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by Lambek. This mathematical framework enables us to compute the meaning of a well-typed sentence from the meanings of its constituents. Concretely, the type reductions of Pregroups are `lifted' to morphisms in a category, a procedure that transforms meanings of constituents into a meaning of the (well-typed) whole. Importantly, meanings of whole sentences live in a single space, independent of the grammatical structure of the sentence. Hence the inner-product can be used to compare meanings of arbitrary sentences, as it is for comparing the meanings of words in the distributional model. The mathematical structure we employ admits a purely diagrammatic calculus which exposes how the information flows between the words in a sentence in order to make up the meaning of the whole sentence. A variation of our `categorical model' which involves constraining the scalars of the vector spaces to the semiring of Booleans results in a Montague-style Boolean-valued semantics.