Semantic representations

[Mark_Johnson at Brown.edu]

I'm writing this from Ron Kaplan's terminal in Holland, and while the
network connection seems to be working, it is a bit slow ... so I will
keep it short.

I want to try to explain why I think the ``problem'' about the
semantic representations ``changing'' in the resource-based accounts
is in fact a non-problem.

IMHO, resource based systems really are about classifying a
configuration of objects.  Sometimes a configuration of objects can
count as a single object, and in the case of adverbial modification,
the configuration of a saturated proposition and an adverb also
counts as a single saturated proposition.

Sometimes I find context-free grammars a useful analogy.  Given
standard toy CFG rules and lexical entries, a utterance ``Mary likes
John'' can be described as a configuration ``NP V NP'', ``NP VP'' or
``S''.  These are just alternative descriptions, and don't stand in
any ordering to each other _as_descriptions_, although particular
parsing algorithms (i.e., proof systems) may prove that ``Mary likes
John'' is an object of type (or category) S by actually enumerating
these structural descriptions in some order.

Now, in the CFG case the objects are structured into a linear order,
but IMHO in semantic interpretation in LFG we should view the
f-structure as imposing a graph structure on semantic objects.  
In Ron's terms, I would like to say that there is a simple
homomorphism from the f-structure to the semantic structure: it is
essentially just the f-structure, viewed as a graph and populated
with ``semantic objects''.  We impose a condition on the semantic
structure: it must be describable as a single semantic object of
type t -- this is precisely the same as requiring that the string
of words be describable by the single category S in the c-structure.

The analogy goes further.  C-structure trees are really nothing more
than normal forms of proofs that the string of words is actually of
type S.  Similarly, there are normal forms for proofs that a
configuration of semantic entities distributed across an f-structure
constitute a single semantic entity of type t.  These normal forms
have the structure of lambda terms (this is the Curry-Howard
isomorphism), and lo and behold, the lambda terms we want as semantic
interpretations for model theoretic interpretation are homomorphic
images of these proofs/lambda terms.

So the resulting system is quite symmetrical (I hesitate to say
``beautiful''), and the semantics is ``derivational'' in precisely the
same sense that the c-structure is.

Comments welcomed!

Best,

Mark



-- 

Mark Johnson, Cognitive & Linguistic Sciences Box 1978 
Brown University, Providence, RI 02912
telephone (401) 863 1670, telefax (401) 863 2616.
preferred email: Mark_Johnson at Brown.edu