Re: Roles and dependence (Pat Hayes)
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Date: Thu, 21 Sep 1995 12:17:07 -0600
To: "Nicola Guarino" <>,,
From: (Pat Hayes)
Subject: Re: Roles and dependence
Cc: "Pat Hayes" <>, "Peter Simons" <>,
        "Barry Smith" <>
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.....(much deleted)

>Coming now to the general position hold by Pat, namely that everything is
>intimately connected with everything else,

No, I didnt say that! Think of knowledge as a huge hypergraph, where the
entity names are the nodes and the facts (axioms) are the hyperedges. (This
is too crude, as it doesnt allow for quantification scope, etc., but just
as an aid to intuition.) Now, talk of 'definitions' and 'primitives'
suggest that there is a small sub-hgraph of this thing from which all the
rest can be derived, a kind of definitional skeleton. The condition you
describe is a different extreme, where every node is pretty directly
connected to every other one. I dont think either of these is right. The
hgraph doesnt have a global skeleton (more correctly, I see no reason to
suppose that it has one.) It is probably connected, but not totally
connected; in fact, its often rather sparse. 

I believe that the notions of
>dependence used above can help to isolate "islands" within this mess: maybe,
>the notion of "clusters" proposed by you, Pat, many years ago, can be
>revisited in order to use some suitable criterion of dependence in order to
>isolate them.
A cluster is a 'place' in the hgraph where it gets to be highly connected,
ie the ratio of facts to concepts gets to be higher than average, ie we
know rather a lot about the interrelationships between these concepts.
(This isnt a precise notion, let me hasten to add, and I wouldnt claim that
it has more than a heuristic utility.) But notice that this is a syntactic
notion: its talking about the structure of the knowledge base itself, not
about the domain being described.


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