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>

To: jborden@mediaone.net

CC: drew.mcdermott@yale.edu, www-rdf-logic@w3.org

Date: Wed, 6 Jun 2001 14:11:45 -0400 (EDT)

Message-Id: <200106061811.OAA26541@pantheon-po04.its.yale.edu>

To: jborden@mediaone.net

CC: drew.mcdermott@yale.edu, www-rdf-logic@w3.org

[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 McDermottReceived on Wednesday, 6 June 2001 14:11:52 UTC

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