How more/less abstract is HPSG?

[Carl Pollard]

Hi Raul,

It seems to me that what is at stake as far as precision is concerned
is not whether (putatively) empirical claims are formalized, but
rather whether it is absolutely clear what is being claimed. Of
course, expressing the claims in a model-theoretically interpreted
formal language is a way to achieve this, and is a way to uncover
hidden vagueness.  Stabler's formalization of GB in first-order logic
is a perfect example of this.

But some constraints are harder to formalize than others. Ones where
the only relation made use of is path equality (e.g.  Head Feature
Principle) are easily expressed in the simplest kind of feature logic
(like Kasper-Rounds logic). Things get harder when you bring in more
complicated relations like append (e.g. Valence Principle) and
quantifiers (e.g.  Binding Principles A and B). That is the whole
point of RSRL (relational speciated reentrant logic -- Richter 2000),
which is a feature logic with relations and quantifiers and an
explicit model theory in which constraints like the Valence Principle
and the Binding Principles can be expressed formally. But this
language did not exist in 1992. The closest thing back then was
programming systems like ALE, CUF, TFS, etc. (Well, technically, Paul
King's language SRL could be used to express such things, but only if
one employed not-linguistically-motivated features---so-called `junk
slots'---to store the results of intermediate computations.  I don't
think you would not want to have to write your whole grammar in SRL,
except maybe as a character-building exercise.)  All of this is
discussed at length in Richter 2000.

As for your comment about staying humble about HPSG's remaining (and
numerous) formal inadequacies -- indeed. One of my main research foci
right now has to do with fixing what I see as foundational problems
with existing HPSG formalisms. It seems to me that this is likely to
involve taking the advice of Haskell Curry (1961) and Drew Moshier
(mid-90's) and switching to a different kind of logic (a kind of typed
lambda calculus) which has a richer type theory than the ones
that have been used in HPSG so far.


Carl