[HPSG-L] relation between Formal Grammar of Human Language and CFG

[chris brew]

>From the perspective of mathematical linguistics, a key thing to understand
is that the various mathematical formalisms (regular grammars, CFGs, mCFGs,
CCG, TAG etc.) are all means of defining
sets of allowable sentences. Usually, these sets are infinite. From the
perspective of grammar theory, the key question is "which of these classes
of infinite sets do we want to talk about?"

Carl Pollard's answer is: there is no principled limit on what grammar
theorists might want to talk about, so we should use formalisms that can
talk about anything at all. While he was teaching at Ohio State, he used to
offer seminars that included the use of category theory, which is a very
general theory of mathematical objects and their relations. Category theory
is a useful tool for finding and analyzing similarities and differences
between mathematical systems. Things that on the surface look different can
turn out to be fundamentally the same. In particular, there are loads of
formalisms that are powerful enough to talk about anything at all. For a
linguist who agrees with Carl about the need to use one of these powerful
formalisms, the choice can be made on the basis of personal convenience,
familiarity, popularity or other criteria. In my view, HPSG is an excellent
choice in these terms. There is no need to worry about mathematical
differences, because, in a certain sense, there aren't any.

Steve Isard gave me some somewhat similar advice, from the perspective of
"what is true about language?". He pointed out that as you move from
regular grammars up to CFGs and beyond, you add, at each step, the ability
to make many many distinctions between sets. Since each step up the
hierarchy is a big step, and we don't really know what the sets defined by
"possible human language" are, we would have to be really lucky if one of
the mathematical objects happened to be a good fit around the set defined
by some formalism. So you either pick a formalism that leaves some
important stuff out (e.g. CFGs) or one that is definitely enough (such as
predicate calculus).

Chris

Footnote: it takes a bit of mind-bending to get used to the idea that it is
possible to say that one infinite set is bigger than another, or that one
infinite set can include another while remaining the same size. But this is
so. The simpler examples, which are really not simple at all, involve
numbers. If you are familiar with the relationships between the set of
natural numbers, the set of integers, the set of rational numbers, the set
of rational and irrational numbers and the set of complex numbers, you will
be prepared to understand the relationships between the formal objects that
turn up in linguistics.


On Fri, Aug 5, 2022 at 11:11 AM Stefan Müller <St.Mueller at hu-berlin.de>
wrote:

> Dear Roussanka,
>
> The general insight from the eightees was that human language is not
> context free. Some people call it mildly context-sensitive. Since GPSG
> was constructed to be context free, people were looking for something
> more powerful and abandoned it in favoure of GPSG. This taken together
> with a more lexical view resulted in HPSG, which has exactly the right
> generative capacity: It has Turing power. =:-)
>
> While CCG and TAG people will tell you that this is way too powerful,
> HPSGians usually have a different view. The formalism should not be
> constraining but the theory formulated within the formalism has to be as
> restrictive as possible. Carl Pollard argued for this in a paper.
>
> The whole discussion and references can be found in the HPSG handbook
> and in my Grammar Theory textbook. I have a (brief) chapter on
> generative power (Chapter 17):
>
> https://langsci-press.org/catalog/book/259
>
> https://langsci-press.org/catalog/book/287
>
> Geoff Pullum has a good paper on the history of the discussion. All
> referenced from with in the book.
>
> Best
>
>      Stefan
>
>
> Am 05.08.22 um 14:24 schrieb Roussanka Loukanova:
> > Dear All,
> >
> > What is the verdict on the relations between Formal Grammar of Human
> > Language and Context-Free Grammar (CFG) of Chomsky hierarchy on formal
> > grammars and languages?
> >
> > I would appreciate very much, opinions, points to research and,
> especially,
> > bibliographical references.
> >
> > Best Regards,
> > Roussanka
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