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Re: [ontolog-forum] FW: Lattice of theories

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>
Date: Sun, 18 Jan 2009 15:01:07 -0800
Message-id: <20090118230203.E4D93138D17@xxxxxxxxxxxxxxxxx>
Len Yabloko wrote:
=============== =============== ================= ==============
John,     (01)

As I said there is more to it than terminology. We still need to nail the
issue of "grounding" raised by Sean.
>LY> T-Box/A-Box distinction is highly reminiscent (to say the least)
> > of class/individual or type/instance.
>The T-box is used to define a hierarchy of types (in Aristotle's
>terminology, 'categories') and the A-box is used to make assertions
>about individual instances that belong to those categories or types.
>LY> I think these are the closest common ancestors to both
> > terminologies - not syllogism.
>Aristotle introduced the method of definition by genus and differentiae.
>For each category (or type), the genus is the supertype and the
>differentiae are the axioms that distinguish a given category from
>other categories with the same supertype.  The syllogisms are the
>patterns of reasoning about the relationships among the categories.
>For this reason, the categories are also called "categorial syllogisms".
You and Pat H. seem to both subscribe directly to Aristotle in claiming that
there is nothing but axioms that distinguish categories/types. It follows
that type vs. individual (aka class vs. instance) distinctions is a matter
of convenience, T-box and A-box are just boxes. Then how do we go about
abstraction? Are you equating generalization with abstraction?    (02)

On the other hand, your two-stage semantics which Pat H opposed so
vehemently in recent thread, seem to suggest that abstraction precedes
generalization. That raises a question about how to apply such
generalization to concrete things in world. Perhaps meta-level reasoning is
your answer. But how do you establish correspondence between statements
about types (ie abstraction) and statements about concrete things. This is
the question of grounding, which neither you or Pat H is interested or able
to answer.    
=============== =============== ================= ==============
[RC] To recast this same thought into currently representative technology, a
database for a commercial web site has a schema or theory (T) and real or
actual data (A) stored in the database.  IMHO, that means the data (A) is
grounded in realities about which the data was captured.  The semantic
theory is the database schema (T).  So (T) represents the present theory of
the universe with respect to this database.      (03)

That implies that (T) is the set of generalizations or abstractions, while
(A) is the set of specializations, or individuals.      (04)

Is this translation to database terminologies equivalent in your opinion?    (05)

-Rich    (06)

Rich Cooper
Rich AT EnglishLogicKernel DOT com    (07)

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