Mereology vs. set theory
sowa@watson.ibm.com
Message-id: <9205141600.AA26334@cs.umn.edu>
Reply-To: cg@cs.umn.edu
Date: Thu, 14 May 92 11:58:38 EDT
From: sowa@watson.ibm.com
To: CG@cs.umn.edu, INTERLINGUA@ISI.EDU
Cc: SCHUBERT@CS.ROCHESTER.EDU
Subject: Mereology vs. set theory
In his note, Len Schubert said
> I just want to point out that the issue of set theory versus
> mereology in NL semantics is far from settled.
This is certainly a major research issue, and as I said in my first
note in this series, I would not propose something so unsettled as a
basis for the ANSI or DARPA standards. However, I believe that people
who are doing research should consider the alternatives.
Chris Menzel and Pat Hayes made the point that set theory has more
structure than mereology, since it distinguishes sets and elements.
But that is true only when you consider them alone without any other
predicates.
As I mentioned in my previous note, if you use FOL plus mereology, you
get a more flexible system than FOL plus set theory. In set theory,
the divisions and subdivisions into elements are fixed. In mereology,
a collection can be subdivided into parts in many different ways.
If you want to fix the subdivision for some purpose, you can do so by
adding extra predicates to mereology, such as cat(x) for selecting the
cat parts of your collection or molecule(x) for selecting the molecules.
For knowledge representation, I would say that the chief difference
between mereology and set theory is whether you construct things
>From the bottom up (as in sets built up from a base collection of
elements) or whether you analyze things from the top down (as in an
undifferentiated plenum, which you take apart by defining selection
predicates). Mereology with selection predicates gives you the same
kinds of structures you can build in set theory, but it allows you
to change your way of looking at the world for different purposes.
John Sowa