Re: ISSUE: Classes as instances

I have written extensively on issues in which the classes as instances 
problem comes up (e.g. [1] and [2]), and also about cases where the "isa" 
relation is misused and another transitive relation is intended (e.g. [3] 
and [4]).  The fact that the latter happens does not remove the need for 
the former, however.

There are a number of well understood canonical examples of when the only 
correct solution is to allow second order predicates.

The "animal/species" example is one.  There is no way to model this 
properly in first order.

In the library domain there a numerous taxonomies, such as the subject and 
genre, which can't be combined (in one system) in first order.

The wordnet and thesauri examples are classic meta-modeling problems, in 
which we have a description of a class of entities whose instances form a 
taxonomy.

In all of these cases, you can invent modeling "hacks" by attempting to 
collapse the is-a relation into a special purpose relation in first order, 
however  by doing so you lose much of the inferential power of the 
language.  This is especially true in description logic like languages 
which FEATURE inference based on the is-a relation.

To argue that there is no need for this is rather silly, really.  I'm 
surprised to see Ian and Peter doing so.  On the other hand, to argue that 
there is a severe computational expense to allowing it IS, in my opinion, 
quite serious.  So, I propose skipping the "well, I think the right way to 
model this is x" arguments, and move on to, "This is the price of allowing 
classes to be treated as instances in the language".

Note that the is-a relation is itself second order, it is a relation 
between classes whose denotation is typically material implication.



[1] Welty, Chris. 1998. The Ontological Nature of Subject Taxonomies. In N. 
Guarino, ed., Formal Ontology in Information Systems. IOS Press Frontiers in AI Applictions Series. 317-327. Trento, Italy. 
June, 1998. Available at 
http://www.cs.vassar.edu/faculty/welty/papers/fois-98/fois-98-1.html

[2] Welty, Chris. 1995. Towards an Epistemology for Software 
Representations. Proceedings of KBSE-95, The Tenth Knowledge-Based Software Engineering Conference. IEEE Computer Society Press. Pp. 148-154. November, 1995. Available at 
http://www.cs.vassar.edu/faculty/welty/papers/software-epist/kbse_1.html

[3] Guarino, Nicola and Chris Welty. 2002. Evaluating Ontological 
Decisions with OntoClean. Communications of the ACM. 45(2):61-65. New York:ACM Press. Available at http://portal.acm.org/citation.cfm?doid=503124.503150

[4] Welty, Chris and Nicola Guarino. 2001. Support for Ontological 
Analysis of Taxonomic Relationships. J. Data and Knowledge Engineering. 39(1):51-74. October, 2001. Available at 
http://www.cs.vassar.edu/faculty/welty/papers/DKE-2001.pdf


Dr. Christopher A. Welty, Knowledge Structures Group
IBM T.J. Watson Research Center
PO Box 704, Yorktown Heights, NY 10598, USA
+1-914-784-7055 Fax: +1-914-784-6078

Received on Friday, 19 July 2002 11:15:14 UTC