[developers] predicate naming in MRS

Ann Copestake aac10 at cl.cam.ac.uk
Fri Jan 1 16:37:37 CET 2016

I'll have a go, but I do realise from previous discussion that you are 
intentionally simplifying, and that some cases where I regard something 
as an unhelpful oversimplification, you may still think this is 
justified.  So, if I may, let me take one example from that page and try 
an explanation, and then see whether we can come to some mutual 
understanding.  This isn't actually anything to do with predicate naming 
conventions, but I want to take a more straightforward case:

> The semantics corresponding to nominals prototypically involves an 
> instance variable and a (generalized) quantifier, which jointly we 
> take to denote a /set/, possibly one of singleton cardinality (for 
> quantifiers introduced by singular determiners, e.g. /a/ or /this/) or 
> even an empty set (for the /no/ quantifier, as in for example /no dogs 
> bark/). 

I take it here that you're talking about the semantics of a phrase like 
"every dog".  If we're interpreting `every' as an ordinary quantifier,  
`every dog' could be written as \lambda P \forall x [ dog(x) => P(x) ]  
- it's of type <<e,t>,t> since it requires something of type <e,t> 
(e.g., an intransitive verb, like barks) to give a truth value.  In 
fact, `every dog' denotes the set of all sets of which the set of dogs 
is a subset (so it does denote a set, but not, I think the one that your 
text would imply). With generalised quantifiers, something similar is 
going on, except that the quantifier is expressed in terms of the 
cardinality of the set of dogs and the set of Ps.

Of course, in MRS, the BODY of the quantifier is missing (and this 
actually means that we can do the composition more straightforwardly 
though I won't go into that here). But that doesn't mean that the MRS 
for `every dog' denotes the set of all dogs.  The semantics we've given 
for MRS is not in terms of real world denotation at all, but in terms of 
how it corresponds to a set of expressions in some object language, 
which might be predicate calculus with generalised quantifiers, but does 
not have to be.  So there is an inconsistency with the MRS paper.  (For 
me, this matters a lot, not least because this object language doesn't 
work as a general account of semantics, although it has its uses.)
But we have never provided a way of giving a semantics for partial MRSs 
in terms of lambda expressions.  (We didn't develop an underspecified 
form of lambda calculus although, if I remember correctly, that's what 
UMRS did.)  Anyway, even talking in an underspecified representation, 
because the body of the quantifier is uninstatiated, I think I would 
still say that an informal gloss of the meaning of `every dog' has to be 
the same as in the fully scoped version - i.e., as above, the set of all 
sets of which the set of dogs is a subset.

So, technically, one cannot talk about an MRS denoting anything in a 
model corresponding to the real world.  If you decide to make a loose 
translation of a partial MRS into the lambda calculus rough equivalent, 
that's OK, though I think you would have to make it much clearer that is 
what you are doing (and the gloss you've given here is incorrect, even 
viewed in that loose way).  To draw an (imperfect) analogy - it's a bit 
like talking about an HPSG in terms of phrase structure trees.  It can 
be a useful thing to do, both in terms of getting points over to 
non-specialists and in talking informally about some analyses, but it's 
vital that it is clear in such a discussion that we are only using the 
trees as some sort of abbreviation and that a syntactician unfamiliar 
with HPSG does not go away with the idea that we are really manipulating 
trees. Something that I hope we (possibly me and Guy) can do in advance 
of the LREC tutorial is to show a translation of an ERS fragment into 
something like a database query application - where quantifiers actually 
matter ... This might make all this clearer.

As I say, I can understand if your reaction to these comments is that 
you're just trying to give an intuition of ERS for people who know no 
formal semantics.  I don't personally think it works to do this (or at 
least, a really informal account might work, but I'd avoid talking about 
denotation in that case) but I understand you feel it is helpful.  If 
you do want me to go through line-by-line and explain the formal issues 
with other parts of the pages, I can do that, but I don't think I should 
start that exercise unless we've got a common idea about the objective.

Happy New Year!


PS - in the paper that Dan and I co-authored in Corbett and Kibort's 
`Feature' volume (which I should put on my website) there is a 
discussion of what might be involved in `translating' ERS into a formal 
account of plurals.  Perhaps this should help to indicate why I think it 
is a very positive feature of *MRS in general (and ERS) that it can be 
translated into different object languages.

On 01/01/2016 00:32, Stephan Oepen wrote:
> a happy new year, everyone!
>> My problem with this document is not so much that it's ERG-specific but that
>> it is in contradiction to the MRS paper in various places.  Which is
>> unfortunate.
> i authored that page jointly with dan and emily, and i do not recall
> intentional deviations from the various publications on MRS.  it would
> be helpful for us to know the specific contradictions you have in
> mind.
> all best, oe

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