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Re: [ontolog-forum] How determine the instances of this concept?

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Ed Barkmeyer <edbark@xxxxxxxx>
Date: Thu, 06 Oct 2011 12:02:01 -0400
Message-id: <4E8DD0F9.4010408@xxxxxxxx>

joel luis carbonera wrote:
> I'm modeling an ontology for the field of geology.
> Trying to represent the ontology in first order logic, considering the 
> necessary and sufficient conditions for each concept, I have found 
> some challenges regarding to a specific concept, called Sedimentary 
> Facies.
> The current domain definition of Sedimentary facies is as follows:
> A Sedimentary facies is a amount of rock in a body of rock, visually 
> distinguishable (through discontinuities of visual properties) of 
> adjacent amounts of rock in the same body of rock.
> How can I formalize this concept in FOL?    (01)

Noting Matthew's suggestion, I think the issue is to "correct" the 
definition so that it can be formalized.  It is not at all clear what 
the intended distinction between "amount of rock" and "body of rock" is, 
or whether there is one.  But in any case the Sedimantary facies is an 
'amount' only in the sense of being a distinguishable body.  What 
Matthew called R = Rock is either 'body of rock' or some more general 
superclass, e.g. 'rock', of which both 'body of rock' and 'sedimentary 
facies' are subclasses.  Matthew then suggests that you need a term for 
'discontinuity of visual properties', which he called 'boundary'.  So 
let us reword the definition to make it clear:    (02)

A sedimentary facies is a 'region of rock' that is part of a 'body of 
rock' and that has a set of 'discontinuity of visual property', such 
that each 'region of rock' that is part of the 'body of rock' and does 
not overlap the sedimentary facies is either not adjacent to the 
sedimentary facies or is separated from the sedimentary facies by/at one 
or more of the discontinuities in the set.    (03)

Note here that I suggest that the distinction of instances of 
sedimentary facies is explicitly based on the mereological concepts 'is 
part of' and 'overlaps' and the spatial concept 'is adjacent to'.  These 
are foundational ideas in spatial ontologies, and they seem to be useful 
here.  Similarly, the idea of a 'boundary' separating 'regions' is 
typical of (geo)spatial ontologies.     (04)

The idea 'discontinuity of visual property' and thus 'visual property' 
are concepts you would have to define.  And therein lies the real 
difficulty:  You probably cannot define 'discontinuity' without 
referring to 'region of rock'.  So the ideas of 'region' and 
'discontinuity' (or 'boundary') are mutually dependent, and they are 
_jointly_ characterized by a set of axioms (and the inevitable appeal to 
physical intuition).  (You may be uncomfortable with this, but it is 
formally very workable.)    (05)

> Apparently, the instances of this concept are determined depending on 
> each other, in a relative way. I'm not sure that I can logically 
> determine what are the instances of the concept.    (06)

There is nothing wrong with instances being determined 'in a relative 
way', i.e., by some 'constructive distinction' from others of their 
kind.  That is the way in which mereologies usually work.  Mereology 
supports the idea of 'overlap' -- that two instances may be 
distinguishable but not physically distinct. Being physically distinct 
-- non-overlapping -- is an additional property.  And "assembling" a 
body of rock from a set of non-overlapping regions depends on how you 
choose the _set_.  It can be selected by some rule from a conceivably 
larger set of well-defined region instances that may have some 
overlaps.  Or you can define regions as instances of such a set, that 
is, such that the definition of each instance depends on the other 
members.  All of those ideas can be separately formalized -- you choose 
the axioms and properties that are useful to your purpose.     (07)

In any case, the instances can be _logically_ determined -- their 
existence can be asserted or proved, and their relevant behaviors can be 
characterized -- but they may not necessarily be 'identifiable'.  To 
identify a region instance, for example, requires the use of some 
properties that are unique to individuals, such as location, which may 
have nothing to do with their definition.    (08)

Put another way, you don't have to build rock formations up from named 
molecules to get a useful formal model.    (09)

One caveat:  You can do this in FOL.  I wouldn't want to assert that it 
can be done in OWL.    (010)

-Ed    (011)

> Best regards.
> Joel Luis Carbonera    (012)

Edward J. Barkmeyer                        Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263                Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263                Cel: +1 240-672-5800    (013)

"The opinions expressed above do not reflect consensus of NIST, 
 and have not been reviewed by any Government authority."    (014)

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