I don't agree that natural language processing is at all related to the symbol
grounding problem.  Symbol grounding, as explained in the provided article,
associates internal symbols with meanings.  In the putative internal language used
by humans (something like linguistics's deep structure), symbols--perhaps
distributed patterns of brain activity--are somehow tied to meanings.  But computers
don't face this problem at all.  Logical predicates need not--and possibly
cannot--have meaning to computers.  The sentence
        father(david,josh).
doesn't connote anything to the computer; it doesn't imply love or filial duty or
the inevitable disappointments of coming to know one's parents.  Similarly, a
computer can determine that
        Give the book.
isn't a grammatical English sentence--not because the meaning of "give" isn't
compatible with the sentence, but because presumably "give" is known to take two NP
arguments, not one.
To reiterate, I don't think NLP and symbol grounding are related because I don't
think that NLP has to--or is capable of--associating symbols with meanings.
(I hope I haven't misunderstood the symbol grounding problem.)