[seek-kr-sms] OWL - taxonomy

[Serguei Krivov]

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/

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