semantics, linear logic

[Mary Dalrymple]

I have been intending to reply to the very interesting series of
messages on semantics and LFG, but haven't had time until today.  I
particularly wanted to respond to Avery's recent message:

    > Another aspect of the use of linear logic for semantics that is
    > maybe worth discussing is that it doesn't seem to me that the
    > proposed semantic representations are intended to be interpreted
    > as a psychological realistic level of linguistic representation.
    > Rather they look to me to be convenient mathematical designators
    > for denotations.  If this is right, then using them is a profession
    > of agnosticism about the existence and nature of linguistically
    > significant representations beyond f-structure and argument-structure.

    > I certainly wouldn't blame anybody for such agnosticism, on the other
    > hand the idea that f-structures connect to a level of `conceptual
    > structure' is certainly worth exploring, raising the issue of what
    > kind of architecture would be best for that.  Maybe linear logic,
    > but many standard assumptions would have to be reconsidered, and
    > either solidly justified or abandoned, for example the use of curried
    > functions to represent predicates.

    > An LFG-based version of DRS theory is the kind of thing I would
    > like to be able to envision (I recall that Mark Johnson and somebody
    > produced one a number of years ago, but it was very limited in
    > scope).

    >   Avery.Andrews at anu.edu.au

I think there is a certain amount of confusion about the status of
linear logic in the approach we have been exploring.  Linear logic is
the language we use for specifying instructions for meaning assembly
-- that is, for specifying how meanings of parts of an utterance are
put together into meanings of the whole utterance.  We have called
linear logic our "glue language" for that reason -- it tells us how to
glue pieces of meaning together.

The question of how to specify instructions for putting meanings
together is different from the question of how those meanings should
be characterized and represented.  In most of our work, we have used
intensional logic to represent natural language meanings -- so in
distinction to the "glue language" of linear logic, which tells us how
to put meanings together, we have the "meaning language" of
intensional logic in which we express the meanings we are working
with.  So the result of a linear logic deduction will be that the
f-structure for a sentence is associated with a formula of intensional
logic that expresses its meaning.

I think the question that Avery is addressing has to do with the
status of these formulas of intensional logic.  The use of intensional
logic as a meaning language brings some associations with it, going
back to Montague's work on natural language semantics.  In some of
Montague's work (e.g. PTQ), sentences are associated with formulas of
intensional logic as an expedient way of representing their meaning,
but the formula of intensional logic is regarded as dispensible,
though handy for making it clear what is going on and allowing the
meaning of the sentence to be represented perspicuously.

However, in our work, we aren't required to use intensional logic as
our meaning language -- we could use any logical language that is
suitable for expressing meanings.  In fact, to illustrate this point,
in our draft paper "Quantifiers, Anaphora, and Intensionality"
(Dalrymple, Lamping, Pereira, Saraswat) we gave an illustration of how
DRT can be used as the meaning language.  This means that after the
linear logic deduction has "assembled" the meanings of the
constituents of a sentence, the f-structure for the sentence is
associated with a Discourse Representation Structure that represents
its meaning.  There also has been some interest in using Situation
Semantics as our meaning language, and we hope to make some progress
on that this summer, with John Fry and Stanley Peters.  I'm very
interested in going further in exploring how flexible our system is
when it is coupled with different semantic theories, and Avery's ideas
about conceptual structure would be very interesting to look at as
well.

 - Mary