# Re: Nests and abstract syntax: Quads vs. nests as sets of Triples

From: Drew McDermott <drew.mcdermott@yale.edu>
Date: Wed, 6 Jun 2001 14:11:45 -0400 (EDT)
Message-Id: <200106061811.OAA26541@pantheon-po04.its.yale.edu>

```
[Jonathan Borden]
This is getting much better. Can we do this all with 4-tuples:

<predicate,subject,object,nest> where each are atoms.

Yes.  The "boundaries" I was talking about are then determined as
follows:

-- Every "nest" atom in a 4-tuple corresponds to a nesting
boundary.
-- A 4-tuple <p, s, o. n> is inside a boundary N if either n=N, or n
is the subject or object of a 4-tuple inside N.

If we want nests to really nest (i.e., not overlap) we will have to
add some constraints (amounting to the rule that N1 and N2 share
4-tuples if and only if either the tuples inside N1 are a subset of
those inside N2, or the tuples inside N2 are a subset of those inside
N1).

Assume we have a set of statements Asserted(), what membership indicates is
merely that the statement is the top level statement in a nest and each web
page defines its own nest.

I.e., the "nest" component of every tuple at the top level of a page is
that page's URI.

So the top level statements are those who are not pointed to by other
statements in the same nest. Assuming the subgraph described by a nest is
acyclic, this works. correct?

I'm not sure I understand this.  I would say "The top-level statements
in a nest are those that are not members of any subnest."  Then to
assert a nest is to assert its top-level statements; stronger
conclusions require knowledge of the content and inferences of the
nest.

The nesting graph should be acyclic, in the sense that two nests may
not be subnests of each other.  We need some stronger constraints as
well.  There are some technical holes that need to be filled in.  For
instance, we've all been assuming that a nest can be pointed to from
multiple places.  That means its contents would be inside multiple,
nonoverlapping nests.  Is that okay?  And then there's this: Can a
nest have free variables?  Presumably the answer is Yes, given Pat's
analysis of quantification.  But then if it's pointed to from multiple
places, it seems to me they must all bind all the free variables.
Could the same variable occurrence end up universally quantified when
reached from one direction and existentially quantified when reached
from another?  Blech.

I'm not sure we're all talking about the same proposal at this point.
Pat wanted tuples to be arguments of tuples, but I seem to have
wandered off into assuming that *nests* would be arguments of
tuples.  Have I grossly missed the point, or is this consistent with
what Pat suggested?  (Pat?)  Obviously nests correspond to
*conjunctions* of tuples, so perhaps I'm okay.

-- Drew McDermott
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Received on Wednesday, 6 June 2001 14:11:52 UTC

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