ONT Reductions Among Relations
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RAR. Reductions Among Relations
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RAR. Note 1
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Subj: Reductions Among Relations
Date: Sat, 14 Apr 2001 19:48:55 -0400
From: Jon Awbrey <jawbrey@oakland.edu>
To: Stand Up Ontology <standard-upper-ontology@ieee.org>
CC: Matthew West <Matthew.R.West@is.shell.com>
One of the things that makes the general problem of RAR seem
just a little bit ill-defined is that you would have to survey
all of the conceivable ways of "getting new relations from old"
just to say what you mean by "L is reducible to {L_j : j in J}",
in other words, that if you had a set of "simpler" relations L_j,
for indices j in some set J, that this data would somehow fix
the original relation L that you are seeking to analyze,
to determine, to specify, to synthesize, or whatever.
In my experience, however, most people will eventually settle on
either one of two different notions of reducibility as capturing
what they have in mind, namely:
1. Compositive Reduction
2. Projective Reduction
As it happens, there is an interesting relationship between these
two notions of reducibility, the implications of which I am still
in the middle of studying, so I will try to treat them in tandem.
Jon Awbrey
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