[seek-kr-sms] OWL - taxonomy

[Nico Franz]

Hi Serguei:

Thanks for your illuminating comments! I'm learning new things. Let me 
try to make sense (mostly) for myself of your points and summarize where 
we are now.

1. Via Plato: intensional definitions are difficult to make and to make 
precise.
=> No question about that, but unlike ostensive definitions the former 
have predictive powers which is partly why (not just) scientists like them.

2. [Example 1] Depending on whether we regard the least inclusive 
elements of a classification (i.e. species in my Cyclanthura example) as 
classes or individuals - both options are possible in OWL - we end up 
having an intentional definition (species as classes) or an ostensive 
definition (species as individuals) for the element that is one step 
higher in the hierarchy (i.e. the genus Cyclanthura). It is possible (in 
OWL) to regard the species at the tips of the tree as both individuals 
and classes, but only so long as we guarantee "strict correspondence" 
between these two views.
=> Does this mean we have to restrict and name upfront the actual 
physical specimens that a species viewed as a class may contain? In 
taxonomy each species name is assigned to a single holotype specimen, 
but of course the intensional definition of that species (i.e. its 
diagnosis) may refer to many specimens, including specimens not yet born...
=> Could you clarify is slightly non-technical what a "strict 
correspondence" of species as individual vs. class means? I don't fully 
understand yet.

3. [Example 2] If Cyclanthura is defined in OWL as the intersection of 
Morphs 12, 25, 27 and Cyclanthura pilosa doesn't have 27, then this 
poses a problem. A solution is to further qualify the definition of 
Cyclanthura (union of 12, 25, 25 plus C. pilosa).
=> I think this is an important intermediate result! It seems fair to 
say that real-life taxonomic ontologies leave considerable space for 
"character evolution", i.e. directional transformation or even loss of 
higher-level properties independently at various lower levels.
=> Your first suggested solution is basically to switch to an ostensive 
definition for C. pilosa since this species does not fully comply with 
the intensional definition of its superclass Cyclanthura. Taxonomists do 
that too to a degree. But at the same time there IS a way to think of C. 
pilosa as having Morph 27. Certainly the critical evolutionary 
preocursors for having Morph27 should still exist in C. pilosa's genetic 
make-up. It is just that another subsequent "mutation" has led to the 
suppression of Morph27 in the phenotype of C. pilosa (the actual visible 
morphology of the beetles in this species).
=> I am wondering whether this point is too academic to push further or 
whether it is a very central issue. Taxonomists often have a very 
complex notion of what a "character" (Morph) is, and as I said there is 
a transformational way to reconcile the fact that C. pilosa doesn't seem 
to have Morph27 yet is still correctly intensionally defined as a member 
of Cyclanthura which does have Morph27.
=> Might be a hard problem to solve...(modal logic?; non-monotonic?; 
please elaborate if you think it's promising). From a perspective of 
taxonomy we wouldn't want to give up on character-based definitions just 
because some members of subclasses "have moved on" in the course of 
evolution and further refined or lost their ancestors features (at least 
phenotypicallly; snakes do have lots of suppressed genes for making legs).

4. [still Example 2] You're pitching various solutions to issue 3. 
("almost all features") to Bertram (Shawn? Dave?) who seems to be busy! 
Your solutions look promising to me, and if the SEEK ontologists can 
agree to pursue one or a few particular solutions more seriously 
(Bertram suggested a "three-variable" method before...) then we could 
try out a small but real taxonomy on it.

5. [Example 3] If we first translate G. undulatus into the intersection 
of all its Morphs and then let it "exemplify" Ganglionus, we can solve 
the common issue of incomplete sampling in taxonomic classifications. 
Another important and encouraging intermediate result!

Thanks again Serguei! Let me know if I got it mostly right or wrong. 
Please continue as your time permits and maybe the others will join in too.

Best,

Nico


Nico M. Franz, Ph.D.
Postdoctoral Research Fellow
National Center for Ecological Analysis and Synthesis
MSB, Room # 3411, University of California
Santa Barbara, CA 93106-6150

Phone: (805) 893-5934; Fax: (805) 893-8062; E-mail: franz at nceas.ucsb.edu
Website: http://www.nceas.ucsb.edu/~franz/


Serguei Krivov wrote:

> Nico et al,
>
> I finally got to the essence of your questions and I would try now to 
> reason about your examples 1,2,3. Before that let us recall an old 
> anecdote:
>
> When Plato gave the definition of man as "a two-footed, featherless 
> animal;" and was much praised for the definition; so Diogenes plucked 
> a cock and brought it into Plato's school, and said, "This is Plato's 
> man." After this incident the addition "with broad flat nails" was 
> made to Plato's definition.
>
> The gist of this is that there is an inherent difficulty in giving any 
> intensive definition that would catch physical reality (not too much 
> difficulty with mathematical reality though). Taxonomists are on the 
> forefront of this difficult battle along with biologists who do 
> ontologies for anatomy and biochemistery. Translating taxonomies into 
> any precise language such as OWL is a pease of work.
>
> The first page of the PDF shows a character-by-taxon matrix in which 22
>
> species (species concepts, strictly speaking) are evaluated for the
>
> presence or absence of 32 morphological features. Each species here is a
>
> class (I assume also in OWL-speak) with a list of properties that
>
> characterize it (and others that it doesn't have).
>
> Let us call them Morph1, Morph2,…,Morph32
>
> So let us look at example 1 - the genus concept Cyclanthura (sec. Franz
>
> in this humble scenario). The genus Cyclanthura may be defined by the 15
>
> species it contains.
>
> If species are at the bottom of our hierarchy then this will be 
> extensive or ostensive definition. If the Specimen are at the bottom 
> of our hierarchy then genus Cyclanthura has 15 subclasses 
> corresponding to each of 15 species. Then suddenly we have intensive 
> definition. We are free to chouse either species or specimen to be our 
> individuals. We can also choose to have both species and specimen to 
> be individuals, but then we have to ensure that there is strict 
> correspondence between species as individuals and species as classes, 
> which is easy in OWL- just introduce some functional property on the 
> class of specimen; Specimen subcllassOf 1:hasSpecies.Species. Here 
> Species is a class that includes all classes cast as OWL individuals.
>
> On the other hand, note that the genus Cyclanthura has three distinctive
>
> features - characters 12, 25, and 27. Those are postulated to have
>
> jointly evolved at the time of the genus' origin according to the
>
> distribution of these features in the 15 species and the phylogeny
>
> algorithm used. So alternatively the genus is defined by those features,
>
> which I call "intensional defining", or defining by "describing".
>
> Let's look at example 2 - Cyclanthura pilosa. This is a species concept
>
> that works (1) as a instance of Cyclanthura (see above), but (2) as a
>
> class which has unique properties by itself. Note that Cyclanthura
>
> pilosa does NOT have feature 27 present as predicated by the
>
> higher-level definition (of the genus Cyclanthura). The phylogenetic
>
> analysis postulates the it has "secondarily lost" that property in the
>
> course of evolution (what we call "homoplasy").
>
> Right we could theoretically write
>
> (*) Cyclanthura equivalent to Intersection( Morph12 Morph25 Morph27)
>
> But that would be wrong from standpoint of OWL, because Cyclanthura
>
> pilosa does not have 27
>
> So I would write for example:
>
> (**)Cyclanthura equivalent to
>
> Union (
>
> Intersection( Morph12 Morph25 Morph27)
>
> {Cyclanthura-pilosa}
>
> )
>
> Question - is this a true inconsistency sense OWL-DL?
>
> No (*) is merely incorrect intensive definition, just like in the old 
> anecdote. Definition (**) and necessary "with broad flat nails"
>
> The instance Cyclanthura pilosa was
>
> supposed to have all distinguishing features of its class Cyclanthura
>
> but in fact it does not (anymore).
>
> OWL could not deal with “suppose”, “necessary” etc. , so this would go 
> to comments on the definition. If it were important to process such 
> information machinery we would need to use modal logic instead of owl
>
> Species in particular have been
>
> called "homeostatic property clusters", meaning that any of their
>
> supposedly defining features could in fact be missing due to
>
> evolutionary change, yet the properties in general are still needed to
>
> define species.
>
> This is a generalization of what we have with Cyclanthura pilosa. I do 
> not see any way to express such fuzziness in OWL. But, from what I 
> know about fuzzy logic- that would not help either. Only non-monotonic 
> logic could handler this situation correctly. In fact non monotonic 
> logic has been invented with this in mind.
>
> Bertram: should we think about non-monotonic version of owl? I am 
> somehow familiar with techniques of non monotonic proofs and can think 
> of non monotonic version of OWL-DL. But that might be an overkill in 
> terms of amount of work.
>
> On the other hand we may think of a design trick that would allow to 
> express this clustering in OWL-DL. Suppose we have individuals 
> IMorph1, IMorph2,…,IMorph32 corresponding to morphological classes. 
> Suppose each morphological class Morph_i is defined via value restriction
>
> Morph_i equivalent Exist hasMorphologicalClass.{IMorph_i}
>
> Property hasMorphologicalClass can have many values
>
> Now suppose C is a collection (enumeration) of morphological features 
> and we believe that any species of genus G has **almost all** features 
> from C. Almost all does not have any meaning in our logic so we would 
> rather say that every species of genus G has at least N-1 (or N-3??) 
> features from C and N is cardinality of C. Then we could define:
>
> G equivalent Intersection(
>
> (All hasMorphologicalClass. C)
>
>>= N-1 hasMorphologicalClass
>
> )
>
> This means that all morphological classes associated with genus G are 
> in C and there are at least N-1 values for property 
> hasMorphologicalClass; this almost equivalent to the statement “ G has 
> almost all morphological features enumerated in C”
>
> And now example 3 - Ganglionus undulatus. This species concept is used
>
> here in a sense to represent the entire genus concept Ganglionus. This
>
> is called "exemplar approach" and is of course very common. It is what I
>
> mean by "incomplete". There are in fact five species of Ganglionus and
>
> most taxonomists would understand me to know this even if I don't say
>
> so.
>
> This is an easy part. First we have to translate the definition of 
> Ganglionus undulates in OWL from one based on the matrix.
>
> “Ganglionus undulates” belongs to
>
> Intersection(Morph1 Morph2 Morph8 Morph9…)
>
> OWL does not have definition by example but that could be introduced 
> as meta owl operation. Basically we have two sentences:
>
> “Ganglionus undulates” belongs to
>
> Intersection(Morph1 Morph2 Morph8 Morph9…)
>
> “Ganglionus undulates” exemplify “Ganglionus”
>
> Meta operation is merely taking RHS of first and second statements and 
> equating them:
>
> “Ganglionus” equivalent Intersection(Morph1 Morph2 Morph8 Morph9…)
>
> Again, this is outside of OWL, but that is too simple to worry about.
>
> Ciao,
>
> serguei
>
> Nico M. Franz, Ph.D.
>
> Postdoctoral Research Fellow
>
> National Center for Ecological Analysis and Synthesis
>
> MSB, Room # 3411, University of California
>
> Santa Barbara, CA 93106-6150
>
> Phone: (805) 893-5934; Fax: (805) 893-8062; E-mail: franz at nceas.ucsb.edu
>
> Website: http://www.nceas.ucsb.edu/~franz/
>