Yes, by 'context', I'm referring to the basis, principles, concerns, ...
with which we are axiomatizing a relation. (01)
In your example, 'part-of' is defined in terms of other relations: (02)
context('part-of') = {'hasSubSequence', ...}
context('hasSubSequence') = { 'isanInstanceOf', 'isaPhysicalPartOf, ...} (03)
If we have shared agreements w.r.t. the meaning of a set of relations,
then we can use these shared agreements to describe a mutually
understandable
context:
- what concepts we share
- what relations we share
- what issues we're talking about (expressed in terms of these
concepts/relations) (04)
Then, we have a basis with which we can reach a consensus w.r.t.
- are we talking about the same concepts and relations?
- although we are talking about the same concepts and relatins, are we
talking about the same concerns (stated in terms of shared
concepts/relations)
... (05)
With enough sharing, we can describe to one another new
concepts/relations/concerns that we can explain on the basis of shared
understanding. (06)
-- Nicolas. (07)
Cassidy, Patrick J. wrote: (08)
>Nicolas,
> I am not sure I understand what you mean by 'context' in your
>comments:
>
>
>
>>>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'.
>>>
>>>
>
> 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:
>
>
>
>>>In the biology context, suppose we define 'PART-OF(A,B)' where A,B
>>>
>>>
>are
>
>
>>>sequences (e.g. DNA, RNA, etc...)
>>>
>>>
>
> . . . 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:
>
> {MouseGenome hasSubSequence ATCCGTACGCCTAGGTTA}
>
> 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:
>
> {NormalMouseGenome hasSubSequence ATCCGTACGCCTAGGTTA}
>
> 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.
>
> 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:
>
> {{?Seq1 hasSubSequence ?SubSeq} impliesThat
> (If {?Oligonuc1 isanInstanceOf ?Seq1) then
> (thereExistsAtLeastOne ?Oligonuc2 suchThat
> {{?Oligonuc2 isanInstanceOf OligoNucleotide} and
> {?Oligonuc2 isaPhysicalPartOf ?Oligonuc1}}))}
>
> 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).
>
> 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.
>
> 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.
>
> 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.
>
> 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.
>
> To reiterate the question: is this the sort of thing you meant by
>needing more "context" for the part relation?
>
> Pat
>
>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
>
>
>-----Original Message-----
>From: ontac-forum-bounces@xxxxxxxxxxxxxx
>[mailto:ontac-forum-bounces@xxxxxxxxxxxxxx] On Behalf Of Nicolas F
>Rouquette
>Sent: Monday, October 31, 2005 3:54 PM
>To: Barry Smith
>Cc: ONTAC-WG General Discussion
>Subject: Re: [ontac-forum] Surveyed Ontology "Library" Systems
>
>Barry Smith wrote:
>
>
>
>>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
>>
>>
>
>
>
>>up out of instances organized (in complex ways) by types.
>>
>>
>
>Ouch... Perhaps I have improperly made a reference to your paper
>(http://ontology.buffalo.edu/concepts/ConceptsandOntologies.pdf)
>in which you state:
>
>"The following figure illustrates the different worlds of concept
>systems, ontologies and
>the information models."
>
>and show a figure with captions:
>
>a) "The world of concepts - meaning of terms"
>b) "The real world of entities"
>c) "The world of information about the real world"
>
>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?
>
>
>
>>>When we use 'part-of' at the instance level to be ontologically
>>>
>>>
>accurate
>
>
>>>in the sense of Barry,
>>>we are still vague about what is the criteria by which we adjucate
>>>
>>>
>on
>
>
>>>parthood. This goes
>>>back to issues of defining criteria of identity and unity.
>>>
>>>
>>Every descriptive/scientific endeavor will face cases where instances
>>
>>
>
>
>
>>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.
>>
>>
>
>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'.
>
>We can specify the meaning of a relationship on an axiomatic basis like
>
>you describe below.
>This amounts to requiring that (b) is an axiomatized ontology.
>
>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
>
>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).
>
>
>
>>>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!
>>
>>
>
>It seems to me you are reading me a bit too litterally.
>
>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'.
>
>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'.
>
>If it is established that we already share the same 'identity'
>criteria,
>then it is clearly unecessary to go through alignment of
>frame/context/whatever 'thing'
>includes metaknowledge about 'identity' and whatever other
>meta-property
>criteria
>we need to share to understand one another's symbols and meanings.
>
>
>
>>>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
>>>
>>>
>what
>
>
>>>should we be doing next.
>>>
>>>
>>Don't let worries about the problematic cases keep you from doing
>>
>>
>good
>
>
>>work with the non-problematic cases.
>>
>>
>>
>The problematic cases are twofold:
>
>- specifying the meaning of axiomatized relationships w.r.t. some
>metaknowledge about (b)
>- communicating the basis of such specifications across agents (people,
>
>machines, databases, etc...)
> where we care to ensure that meaning is preserved across
>communication.
>
>
>
>>>In this example, suppose we want to practically account for the
>>>
>>>
>meaning
>
>
>>>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:
>>
>>PART-OF(A,B)
>>
>>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
>>
>>
>
>
>
>>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
>>
>>
>
>
>
>>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
>>
>>
>
>
>
>>always be defined through the instance level.
>>
>>But if any members of the list have a better account of how
>>
>>
>type-level
>
>
>>relations are to be defined, I would be pleased to hear what it is.
>>
>>
>
>As far as modeling relationships on an axiomatic basis, I'm OK with
>what
>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.
>
>In the biology context, suppose we define 'PART-OF(A,B)' where A,B are
>sequences (e.g. DNA, RNA, etc...)
>
>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.
>
>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.
>
>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
>
>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
>
>came from c456. Perhaps Barry would argue that Nicolas' PART-OF
>relationship should be called something else. The point here is that in
>
>order for us to recognize that Barry and Nicolas have the same
>axiomatic
>formalization of their respective 'PART-OF(x,y)' relationships defined
>over the same domains for x & y, these two relationships clearly
>express different properties.
>
>I believe my concern is still unanswered at the practical level which I
>
>venture to summarize as follows:
>
>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
>
>interepreted?
>
>With doubts,
>-- Nicolas.
>
>
>
>>With greetings
>>Barry
>>
>>
>>
>>
>>
>>
>
>
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