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Message-id: <199508011437.JAA18322@firewheel.cs.utexas.edu> From: pclark@cs.utexas.edu (Peter Clark) Date: Tue, 1 Aug 1995 09:37:21 -0600 X-Mailer: Mail User's Shell (7.2.5 10/14/92) To: phayes@cs.uiuc.edu Subject: Re: Good and Bad IS-A hierarchies Cc: cg@cs.umn.edu, srkb@cs.umbc.edu Sender: owner-srkb@cs.umbc.edu Precedence: bulk

>>>>> There is no way to organize the concepts, or even the axioms, into neat >>>>> little packets so that the various alternatives can be assembled by >>>>> choosing some and ignoring others. [Pat Hayes] >>>> Well, the above paragraph ignores the idea of being able to >>>> compose representations from components. [Peter Clark] >>> It doesnt ignore it, it reports a sober conclusion that that is impossible. >> It might help to distinguish picking-and-choosing axioms which have >> different underlying assumptions about the world, and picking-and-choosing >> axioms which have the same underlying assumptions. Your >> time-interval example was an example of the former. > Thanks, that gives a nice way to sum up my worry: EVERY set of axioms > embodies a different set of assumptions about the world. What is a set of > assumptions other than a set of axioms? Hmmm....yes, I see what you mean. I was worrying about that too. Let my try again: An assumption is a belief about how a theory's symbols map onto the real world ***. Consider your temporal example again: A1: I starts J iff.... A2: intervals are reversible You say that adding A2 means A1 now needs to be revised. But why? It's not that A1 has suddenly become false (axioms are all true in their theory, by definition). It's because that the symbol "start" no longer reflects what you intended it to mean. Consider two (syntactically isomorphic) sets of axioms to illustrate this: AXIOM SET S1 AXIOM SET S2 A1: flowers are pretty A1: cats are good-domestic-pets A2: roses are flowers A2: lions are cats S2 is meant to mimic your temporal example. After seeing A2, I say "oh, you mean cat as in cat *species* (rather than small fluffy thing). Okay, that's fine..," (I don't really mind, just as I don't really mind if temporal intervals are reversible or not), "....but I better go and revise A1 then." Why does A1 in S2 need revising, but A1 in S1 not? There's two notions of "truth" here: 1. truth within a theory (in or derivable from that theory) 2. truth about whether a theory reflects (our beliefs about) the real world, ie. whether statements in a theory are true in the real world, under some mapping of the theory's symbols to the real world. A good set of axioms (eg. S1), under some mapping, is a good approximation to the real world (ie. most true statements in the theory are also true in the real world under that mapping). If I want to drop axioms from that theory, then that's okay: I've just said less, and the theory will be a poorer reflection of the world. I can pick-and-choose happily within this set. I can't do that with S2 though -- the mappings from axiom symbols to the real world conflict. Maybe you *can* pick-and-choose from your temporal theories too. Suppose I take temporal theory T1, and I drop an axiom. Now T1 doesn't say everything I intended it say about time -- but that's okay, it's just now a poorer description of time. You might be tempted to reject the reduced T1 because it no longer says everything you intended to say about time, but that's unfair: how do you know when you've said everything anyway? (Though I take your point about these temporal theories being "minimal" -- it might be that taking out any single axiom will make the theory next-to-useless as nothing can be derived any more, but that doesn't invalidate it). Saying an assumption is some non-axiom-based notion is probably going to land me in trouble -- eg. how can I convey to you what I meant the symbols to mean, other than write axioms? I'm not really sure of the answer; though people can communicate and at least have some agreement on what linguistic symbols mean. And you yourself introduced a mapping when you stated your "I starts J" axiom needed revising. Can I pick-and-choose from my S1-like axiom set now? Best wishes, Pete Footnote: *** or, more precisely: An assumption is a belief about how a theory's symbols map onto my perception of the real world. Really, we're talking about a mapping between two symbol systems (the KB of axioms, and the axioms/symbol system in an agent's head). But I'll just use "mapping onto the real world" for conciseness in this message. --- Peter Clark (pclark@cs.utexas.edu) Department of Computer Science tel: (512) 471-9565 University of Texas at Austin fax: (512) 471-8885 Austin, Texas, 78712, USA. Some WWW pointers to KBS labs: http://www.cs.utexas.edu/users/mfkb/related.html