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RE: [ontac-forum] Surveyed Ontology "Library" Systems

To: <nicolas.rouquette@xxxxxxxxxxxx>, "ONTAC-WG General Discussion" <ontac-forum@xxxxxxxxxxxxxx>
From: "Cassidy, Patrick J." <pcassidy@xxxxxxxxx>
Date: Mon, 31 Oct 2005 20:01:31 -0500
Message-id: <6ACD6742E291AF459206FFF2897764BE5F3002@xxxxxxxxxxxxxxxxx>
   I am not sure I understand what you mean by 'context' in your
comments:    (01)

>> Indeed, this is a reasonable strategy to follow.
>> However, it is nonetheless insufficient w.r.t.
>> how to deal with the 'context' behind the meaning of
>> relaitonships like 'part-of'.    (02)

  There are many things we would like to say that include some notion
of parthood, but many of those are best said by using a specialization
of the "part" relation.  In this case, what I think you mean by
"context" would be captured in the axiomatization of the relation
itself.  In the DNA case you mentioned:    (03)

>> In the biology context, suppose we define 'PART-OF(A,B)' where A,B
>> sequences (e.g. DNA, RNA, etc...)    (04)

 . . .  to be precise and capture the actual meaning of, for example, a
subsequence relation, one would need a specialized relation; call it
for argument "hasSubSequence".  This would be a "subrelation" of
has_part. If it is intended to be used to refer to genomic information,
rather than to apply to individual molecules, then it would have to be
defined as applying either to an abstract representation of nucleotide
sequences, or to a specially defined class of polymer molecules all
having the same composition, which would be an instance of a metaclass
of In this case) "DNA_Molecule", for example.  But the axiomatization
would have to capture all of the intended relations and their
consequences.  Then if we had a class "MouseGenome" representing all
physical Mouse genomes (the DNA part), it might be tempting to say
(using the ESKIF braced notation, a variant of SKIF, a first-order
logic notation)that:    (05)

       {MouseGenome hasSubSequence ATCCGTACGCCTAGGTTA}    (06)

  This might not be true in all cases, even if a normal mouse genome
had that sequence in it.  There might be mutants around.  We would have
to define a subclass of all Mouse Genomes, call it "NormalMouseGenome".
Then we could say:    (07)

       {NormalMouseGenome hasSubSequence ATCCGTACGCCTAGGTTA}    (08)

   This might be true (some genomes do have it).  But the meaning
"NormalMouseGenome" itself would have to be axiomatized, which would
include some probability assertions.    (09)

    How you would axiomatize "hasSubSequence" would depend on the
structure of the class on which it is defined.  If the relation is
defined as having a "signature" (argument types) of
NucleotideSequenceClass and NucleotideSequenceClass, then we might say
something like this:    (010)

    {{?Seq1 hasSubSequence ?SubSeq} impliesThat
     (If {?Oligonuc1 isanInstanceOf ?Seq1) then
         (thereExistsAtLeastOne ?Oligonuc2 suchThat
            {{?Oligonuc2 isanInstanceOf OligoNucleotide} and 
             {?Oligonuc2 isaPhysicalPartOf ?Oligonuc1}}))}    (011)

   This means that every genome which is one physical set of DNA
molecules of one normal Mouse cell has at least one component
oligonucleotide somewhere in its sequence that has that specific
sequence (assuming that the name of a sequence is the same as the
actual sequence, which can be a naming formalism used).    (012)

  But isaPhysicalPartOf would also have to be axiomatized, and for
physical objects it would specify, for example, that if P is part of W
at time T, then wherever W is at time T, P must also be, and P cannot
weigh more than W at time T, and P cannot have a longest dimension
greater than that of W at time T, among other things.    (013)

  As written the axiomatization of hasSubSequence is not quite true,
since an isolated oligonucleotide actually has a fully satisfied
valence, whereas the "part" of the DNA molecule that is still inside
the "whole" would have a slightly different electronic or atomic
structure at the ends than would an isolated oligonucleotide.  But this
can be rectified with more detail, or by using abstract nucleotide
sequences.    (014)

   The point is, that in many cases when we want to specify that
something is part of something else, there is a great deal more that
one can say than just "it's a part", and people knowledgeable about
physical objects understand all those details, even when they don't
need to be so explicit.  For the machines to take over a significant
part of human information-processing effort, they have to understand it
too, which at the present state of the technology means that we have to
tell it to them in all its gory detail.    (015)

   Of course, some very simple reasoning tasks may not need much
detail, and we would not expect most people entering knowledge to get
involved in writing such axioms - that would be a task for a good user
interface.  But we do have the logical mechanisms to specify such
detail when needed, so as to permit the machines to reason accurately
about the information they have.  To do the reasoning as well as we
would like may require that we specialize relations like "part" and
axiomatize them so as to be very explicit about what we mean in each
distinguishable case.    (016)

    To reiterate the question:  is this the sort of thing you meant by
needing more "context" for the part relation?    (017)

   Pat    (018)

Patrick Cassidy
MITRE Corporation
260 Industrial Way
Eatontown, NJ 07724
Mail Stop: MNJE
Phone: 732-578-6340
Cell: 908-565-4053
Fax: 732-578-6012
Email: pcassidy@xxxxxxxxx    (019)

-----Original Message-----
From: ontac-forum-bounces@xxxxxxxxxxxxxx
[mailto:ontac-forum-bounces@xxxxxxxxxxxxxx] On Behalf Of Nicolas F
Sent: Monday, October 31, 2005 3:54 PM
To: Barry Smith
Cc: ONTAC-WG General Discussion
Subject: Re: [ontac-forum] Surveyed Ontology "Library" Systems    (020)

Barry Smith wrote:    (021)

> Responding to Nicolas and Denise:
>> >I also do not think, though, that the relationships I have seen 
>> defined by the
>> >ontology community are sufficiently rigorous to meet the needs of 
>> individual
>> >domains.
>> >
>> Do you have an idea about what's missing?
>> Barry distinguishes 3 worlds of things:
>> - concept systems (describing the meaning of terms w.r.t. relations
>> among terms)
>> - real-world entities (instances & types organized in an ontology)
>> - information models about the world (e.g., an allegorical document)
> Better not to call these three worlds. There is only one world, built    (022)

> up out of instances organized (in complex ways) by types.    (023)

Ouch... Perhaps I have improperly made a reference to your paper
in which you state:    (024)

"The following figure illustrates the different worlds of concept 
systems, ontologies and
the information models."    (025)

and show a figure with captions:    (026)

a) "The world of concepts - meaning of terms"
b) "The real world of entities"
c) "The world of information about the real world"    (027)

Are you saying you don't like your own terminology?
Ok, I'm being picky here. Seriously though, can you please
suggest a better terminology to refer to (a), (b), (c)
that is succinct enough yet precise enough to avoid
the trap I fell into?    (028)

>> When we use 'part-of' at the instance level to be ontologically
>> in the sense of Barry,
>> we are still vague about what is the criteria by which we adjucate
>> parthood. This goes
>> back to issues of defining criteria of identity and unity.
> Every descriptive/scientific endeavor will face cases where instances    (029)

> clearly stand in a given relation (e.g. my heart part-of me); other 
> cases where they clearly do not stand in this relation (e.g. NOT: my 
> heart part-of the Arc de Triomphe); and yet other cases where it is 
> hard to tell (e.g. ?: my heart part-of ONTAC-WG)
> My advice to all is to concentrate initially on the first group of 
> cases (low hanging group). Certainly you should not allow the 
> existence of the third group to block your efforts from the start.    (030)

Indeed, this is a reasonable strategy to follow.
However, it is nonetheless insufficient w.r.t.
how to deal with the 'context' behind the meaning of
relaitonships like 'part-of'.    (031)

We can specify the meaning of a relationship on an axiomatic basis like    (032)

you describe below.
This amounts to requiring that (b) is an axiomatized ontology.    (033)

Your advice implies that an axiomatization of (b) will be done w.r.t. 
certain assumptions and criteria
of modeling granularity, dependence, rigidity, etc... That information 
is not part of the axiomatization
of an ontology. It is meta-knowledge about the axiomatization of an 
ontology that I'm advocating
should be explicitly and declaratively specified relative to something 
else (e.g., (a) or (c)).
This metaknowledge is important to make sure that two agents (e.g., you    (034)

and I) can reach
a consensus about how we are interepreting the axioms of a given 
relationship (e.g., the 'part-of' relationship you describe below).    (035)

>> We need identity to make sense of "a123 part-of b456". How do I
>> recognize 'a123' among all possible instances?
> Typically it will be you who has baptised the relevant instance by 
> using this designation. Thus you may have baptised your heart as 
> 'a123'. If you do not know what instance 'a123' stands for, then do 
> not use this instance designator in your work!    (036)

It seems to me you are reading me a bit too litterally.    (037)

By 'identity', I'm referring to criteria that *I* have established as 
the axiomatic
basis with which I can tell which unique entity in the real world 
correspond to 'a123'.    (038)

I need to be able to communicate these 'identity' criteria to *you* to 
make sure that,
as long as you are reasonable, you are able to recognize which 
real-world entity
corresponds to my symbolic designator: 'a123'.    (039)

If it is established that we already share the same 'identity'
then it is clearly unecessary to go through alignment of 
frame/context/whatever 'thing'
includes metaknowledge about 'identity' and whatever other
we need to share to understand one another's symbols and meanings.    (040)

>> I have a feeling that, at a coarse level, we're more or less in 
>> agreement.
>> At a practical level, there are wholes that are problematic w.r.t
>> should we be doing next.
> Don't let worries about the problematic cases keep you from doing
> work with the non-problematic cases.
The problematic cases are twofold:    (041)

- specifying the meaning of axiomatized relationships w.r.t. some 
metaknowledge about (b)
- communicating the basis of such specifications across agents (people,    (042)

machines, databases, etc...)
  where we care to ensure that meaning is preserved across
communication.    (043)

>> In this example, suppose we want to practically account for the
>> of the 'part-of' relationship at the instance level
>> (i.e., the 'part-of' relationship in the ontology of real-world 
>> entities)
>> - in 'conventional' ontologies, we'd have things like:
>> owl:Class A
>> owl:Class B
>> part-of: A -> B
>> A a123
>> B b456
>> part-of(a123,b456)
> The issue is how does the part-of relation between A and B, which we 
> might write:
> relate to the part-of relation between given instances, say:
> part-of(a123,b456)
> My answer is as follows:
> PART-OF(A,B) =def for every instance a of A there is some instance b 
> of B which is such that part-of(a,b)
> In brief: all As are part-of some Bs
> This is simplified somewhat since it does not take account of time. 
> However, the detailed (all-some) account is still quite simple (see 
> http://genomebiology.com/2005/6/5/R46), and has the advantage that it    (044)

> applies in just the same way to all the so-called associative 
> relations. Thus for example
> LOCATED-IN(A,B) =def for every instance a of A there is some instance    (045)

> b of B which is such that located-in(a,b)
> In brief: all As are located-in some Bs.
> I believe that this all-some approach is consistent, too, with the 
> underlying idea of Description Logic, where type-level relations must    (046)

> always be defined through the instance level.
> But if any members of the list have a better account of how
> relations are to be defined, I would be pleased to hear what it is.    (047)

As far as modeling relationships on an axiomatic basis, I'm OK with
you say.
As far as relating the meaning of relationships modeled according to 
different criteria that are
largely compatible but that have some differences, we then get in to 
trouble quickly.    (048)

In the biology context, suppose we define 'PART-OF(A,B)' where A,B are 
sequences (e.g. DNA, RNA, etc...)    (049)

The 'PART-OF' relationship then allows us, for example, to talk about 
'viral infection scenarios' for example:
i.e., whether a virus has incorporated itself into a host chromosome.    (050)

This perspective is relevant to analyze the viral immunity of certain 
chromosomes or the effectiveness of
various mechanisms against viral infection. In this context, it is 
reasonable to expect the 'PART-OF' relationship
to satisfy the following logical property: PART-OF(v123,c456)=true if 
and only if virus v123 has infected chromosome c456.    (051)

Yet, there is a closely-related context where we might want to 'trace' 
the origin of a particular virus that has managed to clone itself
from a host chromosome and is therefore 'out there' on the prowl for 
infecting other chromosomes, perhaps in the same cell, perhaps
in a different cell. It would be conceivable that someone, e.g., 
Nicolas, would use PART-OF(v123,c456) with the same axiomatic basis
as yours to talk about v123 as a copy of the same virus in c456; except    (052)

that here, v123 isn't chemically bonded within
the structure of chromosome but instead is the result of cloning a 
virus, say, v12, that is chemically bonded within the chromosome c456.
Perhaps Nicolas doesn't really care about v12 after all, only that v123    (053)

came from c456. Perhaps Barry would argue that Nicolas' PART-OF
relationship should be called something else. The point here is that in    (054)

order for us to recognize that Barry and Nicolas have the same
formalization of their respective 'PART-OF(x,y)' relationships defined 
over the same domains for x & y, these two relationships clearly
express different properties.    (055)

I believe my concern is still unanswered at the practical level which I    (056)

venture to summarize as follows:    (057)

Given reasonable axiomatizations of relationships, what additional 
information about each relationship do we need
to specify the range of contexts where that relationship is meant to be    (058)

interepreted?    (059)

With doubts,
-- Nicolas.    (060)

> With greetings
> Barry
>    (061)

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