The syntax-semantics correspondence and underspecification

[Shalom Lappin]

Hi Carl,
     Thanks for this reply. It is worth noting that the first option
that you mention "(1) give different scopings the same tectostructure
and have interpretations themselves be underspecified entities a la MRS
etc." can be applied within a lambda calculus model of grammar, although
one distinct from current versions of CG. van Eijk (2003), Computational
Semantics and Type Theory (ms, CWI, Amsterdam) constructs such a model
which he specifies in a  functional programming (Haskell) framework. Jan
gives underspecified scope representations as lambda terms in which a
function is applied to a list of scope operators and a relation (the
propositional core of a sentence) to yield the list of all resolved
scope readings. The function does not have to be fully computed at run
time, as Haskell uses lazy intepretation in which only a particular
element (or elements) of the list of scope readings are identified, and
this computation can be delayed until an appropriate point in the
interpretation process. Chris Fox and I adopt and develop this approach
in our work on Property Theory with Curry Typing, which is also a lambda
calculus based theory of semantic representation. Regards.

Shalom

Carl Pollard wrote:

>Hi Shalom,
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>I am puzzled by Carl's recent replies to Tibor. Carl you appear to
>have returned to a classical Montague (PTQ) view of the
>syntax-semantics correspondence in which differences in semantic
>representation entail distinctions in syntactic structure. On this
>approach variant scope readings are obtained from alternative
>syntactic derivations/structures.  Have you, then, given up
>underspecified semantic representations of the MRS (or related)
>variety which can be resolved to different interpretations but
>correspond to a single syntactic source? If so, then what of the
>advantages of underspecified representations, such as the avoidance of
>spurious, unmotivated syntactic ambiguity, achieving greater
>computational efficiency in the interpretation process by not
>generating k!  syntactic-semantic correspondences for k scope taking
>elements in a sentence, etc.? If you have not given up underspecified
>respresentations, how are they accommodated in the Lambek calculus
>type grammar that you have sketched?
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>The view I sketched is indeed neo-Montagovian, not the way he actually
>did things in PTQ but they way he mentioned (in passing, in PTQ) that
>he COULD have done it. The way he ACTUALLY did it was to make
>translation a RELATION between strings and IL expressions, but he
>pointed out that he COULD HAVE just as well have made it a FUNCTION from
>analysis trees (which can be considered tectostructures) to IL
>expressions.
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>But then as always one gets a choice about how to handle the
>interpretive multiplicities (I resist calling them ambiguities, which
>implies making the first of the following choices): either (1) give
>different scopings the same tectostructure and have interpretations
>themselves be underspecified entities a la MRS etc., or (2) have
>disambiguating tectogrammatical operations (such as the scope
>operators used in some kinds of CG) that make a semantic difference
>but not a phenostructural one. The former has the well-known
>computational advantages you allude to, but I have a hunch the former
>(the "unmotivated spurious syntactic ambiguity" approach) might make
>linguistic description easier.
>
>[Of course categorial grammarians don't usually consider ambiguity of
>this kind unmotivated and spurious, since they consider the main point
>of tectostructure to be to drive semantic composition. Lambek even
>goes so far as to say that Curry's tectostructure IS semantics not
>syntax, but this seems to me a misreading of Curry.]
>
>An analogous choice arises in the tecto-to-pheno interpretation: you
>can either (1) put put less stuff into tecto and make phenostructures
>underspecified, or (2) put more stuff into tecto to make the relation
>to (fully specified) phenostructures a function (the usual categorial
>approach). The Dowty-style minimalism we've been discussing
>is of the former kind: the multisets of words (and frozen word
>sequences) are the analogs of underspecified semantic representations,
>and the LP rules are the analogs of "handle constraints" (or whatever
>you want to call the constraints that embody the options for resolving
>an underspecified semantic representation).
>
>Carl
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