At 08:13 PM 10/31/2005, you wrote:
>Yes, by 'context', I'm referring to the basis, principles, concerns,
>... with which we are axiomatizing a relation.
>
>In your example, 'part-of' is defined in terms of other relations:
>
>context('part-of') = {'hasSubSequence', ...}
>context('hasSubSequence') = { 'isanInstanceOf', 'isaPhysicalPartOf, ...} (01)
so a context is a sequence of names of relations? (02)
>If we have shared agreements w.r.t. the meaning of a set of relations, (03)
shared independently of any context? (04)
>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)
>
>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)
If we don't already share an understanding of the relations before
specifying the context, how can we use the relations to specify the context? (06)
>With enough sharing, we can describe to one another new
>concepts/relations/concerns that we can explain on the basis of
>shared understanding. (07)
Still sounds dangerously circular to me.
BS (08)
>Cassidy, Patrick J. wrote:
>
>>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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