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From: Joel Young (jdy_at_[hidden])
Date: 2002-09-06 09:05:01

From: Guillaume Melquiond <gmelquio_at_[hidden]>
> Please remember that Joel's model defines a binary relation as being
> the union of some of the 13 fundamental relations.

Only if the "standard" 13 relations are chosen as fundamental. The
space can be arbitrarily partitioned, but yes, however the partitioning
into fundamental relations is done, relations are defined by disjunctive
sets of those fundamental relations.

BTW, One could have a region which is named "undefined"

From: Guillaume Melquiond <gmelquio_at_[hidden]>
> With Joel's model, this unique universal proxy should compute 13 tests
> to find the zone of the half-plane currently occupied by the two
> intervals; and some of these tests may require 4 number comparisons
> (the position of a point in a rectangle). Obviously, some of these
> number comparisons are redundant. But, I think something like 20 tests
> are required to correctly define the proxy.

Should be able to do this with plain-cutting (binary search) decision
tree to get down to only about 4 or 5 comparisons? It would be much
worse if one used arbitrary figures rather than rectangles to define the
fundamental relations (like a ball around the equality point to be
"close-enough to equal").


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