I quite enjoyed the general style and the informativeness of the booklet, which seems closely related with what we've been learning here as well. One thing I was less sure about was the article's take on natural language syntax, in particular the distinction of "left" and "right" dual (corresponding to the fact that natural languages have linear word orders), which isn't a novel point from the booklet or its direct references but reflects a long-standing approach dating back to the early days of Categorial Grammar.
I guess this is an important point for computational linguistics, but in recent developments of theoretical linguistics (at least in the Chomskyan school) linear order has been almost entirely severed out of the syntax module of human language grammar and relocated to the sensorimotor-based "linearization" module (aka. phonology) instead. A main motivation for this move was that world languages vary a lot in their choices of word order, but this seldom has substantial effects on compositional semantics (e.g. both English "yellow banana" and Spanish "plátano amarillo" mean more or less the same thing). From this perspective the (semantically-relevant part of) syntax is purely hierarchical (sets of sets of sets of...sets) and the "left-right" ordering is only settled when the syntactic structure is "spelled out".
Hence, I was wondering whether NLP researchers with a more mathematically-oriented mind have ever considered simplifying some bits of the logico-categorical toolkit by e.g. taking into account the non-semantic parts (e.g. phonology, pragmatics) of natural language grammar. :-)