Avril, (01)
I agree. I was thinking of the set theories that follow Cantor's
approach, which includes the empty set. (02)
AS> ... to be exact, the graph of all subsets forms a lattice only
> in set theories that incorporate the empty set. If the empty set
> is not included, the graph of all subsets is an irregular acyclic
> graph, without the empty set in the bottom. The same goes when
> discrete mereology is used as the model. (03)
In any case, I just wanted to emphasize that lattices with multiple
inheritance occur very widely, even in set theory. (04)
Some people have objected to multiple inheritance because people
who use it may make mistakes that could cause inconsistencies.
I agree that people often make mistakes. (05)
But the solution is *not* to outlaw multiple inheritance, but to
design tools that automatically derive all the inheritance paths
from the specifications. The FCA tools do that very nicely. (06)
By the way, the implementations of FCA from the mid 1990s were
very inefficient, but the recent implementations are several
orders of magnitude faster. (07)
John (08)
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