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

[Pat Hayes <phayes@xxxxxxx>]

On Jan 16, 2009, at 12:38 PM, Sean Barker wrote:

John

Thanks for your response - I think Len has a good way of expressing my
query, but just to make sure:

Data model - old fashion technology, written in EXPRESS, in this case
ISO 10103-203 - the point I was making was one from the experience of using
older
semantic standards.

Grounding - what the data means in the context of the business processes
that use it. For example, by the term "part" I mean a design for a
physical component of a product, but not the engineering drawing of the
part (which is the presentation of the representation of the shape of
the mechanical design view of a version of the part), although this was the
way
it was interpreted in one well publicised project.

Aside: the STEP construct "Product" has been extensively reused for a
wide variety of configuration items, including document (or drawing).
However, STEP models are grounded in a specific business process, and
the context of 10303-203 specific excludes the interpretation of
"product" as "drawing".

My point is not that the same statements about the world may not be
identically grounded, but that the grounding itself is not defined in
the axioms. Or rather, I have yet to see anything in an ontology that
allows me to state that what you mean by "part" is what I mean by
"part". In fact, computers could calculate forever whether two systems
of axioms are isomorphic, but never decide whether axioms have the same
grounding because ultimately the question is answered by the
<b>behaviour</b> of the people reading the computer output.

I think (probably wrongly) Pat H would say that the truth of an axiom
could be decided by looking at the world

Well, no, I would say that. But I agree, in order to define truth relative to the real (or any other) world, you need more than just the axioms: you also need the interpretation mapping which says how the formal names are related to the things in the actual world. Which I think is saying exactly what you are saying, in practice. 

- the question that I am
raising is - how can we ensure that two people checking the truth of an
axiom check the same part of the world?

We need more than the axioms to do that, indeed. But...

If we don't do that, then we
cannot confirm that the ontologies are the same, even if they have the same
axioms.

No, we can check sameness purely formally. If two ontologies are logically equivalent (which can be checked mechanically) then in any interpretation they will have the same meaning. So as long as you ground the terms of the ontologies in the same way I do, then our ontologies will agree. This is exactly why formal logic is so useful: the conclusions it draws apply independently of how the logic is interpreted in a world, because they can only be valid if they work in every possible interpretation. 

PatH

Sean Barker
Bristol, UK

-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Len Yabloko
Sent: 15 January 2009 23:19
To: [ontolog-forum]
Subject: Re: [ontolog-forum] FW: Lattice of theories


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Sean and John,

Sean,

All the ontologies that have been proposed so far have been collections

of statements (often called axioms) in some version of logic.

I think that you are talking about different ontologies here.
Using Semantic Web terminology the set of axioms is called "T-Box"
(if I not mistaken "T" refers to taxonomy or terminology or both) The is
also so called A-Box http://en.wikipedia.org/wiki/ABox

I have noted the use of standard data models to exchange

incompatible data - incompatible not because the data structures

were different, but because the groundings of the model were

different.

I don't know what you mean by the word "grounding" or the term "data

model".

It seems that Sean is calling T-Box a "data model" and his concern is
that the lattice of T-Boxes is not useful for some reasoning with
A-Boxes.
What may be called a "grounding" is this context is another structure
(may be lattice) that orders A-Boxes. Then the question may be: how do
these different structures relate and what to call them. I don't know
the answer.

If by grounding, you mean some part of the world for which some set of

statements (or axioms) are true, then two identical sets of statements

would be true of exactly the same parts of the world.  Therefore,

identical axioms would have identical grounding.

If we accept T-Box/A-box distinction, the the statement above is not
necessarily true.

I don't know whether there is some confusion of terminology or a true

disagreement.

Neither do I. May be Pat H can help us.

John

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