Sean (01)
>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". (02)
I think what allows you to state that is what John calls a lattice of theories.
Using any theory that subsumes the theory you have used to define "part" would
not contradict your definition. The lattice defines some form of type "safety".
But that has to be stated somewhere else. The question is - where? (03)
>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.
> (04)
I have been using the term 'grounding' as some form of agreement between people
that allows certain unifying assumptions. In other words - theory. But without
lattice of some other computable relation people can't find this agreement. (05)
>I think (probably wrongly) Pat H would say that the truth of an axiom
>could be decided by looking at the world - 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? If we don't do that, then we
>cannot confirm that the ontologies are the same, even if they have the same
>axioms.
>
>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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> (06)
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