On Mar 15, 2006, at 10:05 PM, Uschold, Michael F wrote:
I agree that relative interpretability is important. But who uses the
word "subsumption" for it?
Chris Menzel says:
Probbly no one; but -- ignoring the fact that the term is deeply
entrenched in AI/KE literature -- conceptually speaking, "subsumption"
is surely a reasonable term for relative interpretability; surely there
is a reasonable sense in which, say, ZF subsumes Peano Arithmetic.
While you may well come up with a logical rational basis for using the
term 'subsumption' for this, I think it is a bad idea (socially) since
it is likely to cause a lot of confusion.
And of course I agree, though perhaps I was not clear enough. I was not at all suggesting that it be adopted for general use as a synonym for relative interpretability -- note the acknowledgement that it is deeply entrenched already — too deeply to be considered for public term consumption. My point, once again, was only that, conceptually speaking, "subsumption" is a good piece of ordinary English to capture the general relationship that holds between theories like ZF and PA when one is interpretable in the other.