SUO: Re: General Design
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David Holliday wrote:
>
> Jon,
>
> I sort of agree with you, but also believe axioms
> can be discovered with some due diligence.
Sure, but whether it takes six weeks or six million years, the question is:
What is the form of the reasoning process by which you, or your whole species,
work toward the axiomatic definition that captures the nature of the thing?
Most likely it's a complex cyclic process, involving many different types
of reasoning. But what are the irreducible types of reasoning, anyway?
If the total reasoning process is not purely deductive, then a forward
cranking theorem prover is not going to do all the work for you. QED.
Jon Awbrey
> For example, I read 10 or more books on a particular subject, and then
> produced their essence in a new one. This took six weeks, a lot of notes
> and somebody other than I who could actually type.
>
> I was also in charge of a team tasked with defining
> the ultimate CASE tool.
>
> What a nightmare. Over 2000 requirements were proposed.
> I said there were only two: 1) Can you build any software
> with your case tool? 2) Can you therefore build your case
> tool with your case tool?
>
> Of course large companies trying to sell use case tools said this was
> impossible, so I had to prove them wrong. Then I left this large,
> nameless Pacific Northwest aerospace company with the rights to the
> model I constructed. And, it's worked just fine for me.
>
> The original problem was dealing with recursive patterns; people just
> are not used to doing such. Once I got the hang of it, it was easy.
>
> Oh, consider that what appears to be an existing axiom
> might really be a metaphor for something else ;<)
>
> Best wishes,
>
> -David
>
>
>
> -----Original Message-----
> From: protege-discussion-bounce@SMI.Stanford.EDU
> [mailto:protege-discussion-bounce@SMI.Stanford.EDU] On Behalf Of Jon
> Awbrey
> Sent: Tuesday, August 12, 2003 5:16 AM
> To: John F. Sowa
> Cc: cg@cs.uah.edu; Ontology; protege-discussion@SMI.Stanford.EDU; SUO
> Subject: [protege-discussion] Re: General Design
>
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> John, Rich, et al.
>
> The axioms get in the way when you try to put them first.
>
> The axioms are the cart and experience is the horse.
> I guess recalcitrant experience is the donkey or mule.
> The "logical" order of axioms and experience, as if the
> concepts generated the data, is a put-up job. It is the
> order that you rearrange the refined axioms and the raw
> experience into, but only "after the fact", so to speak,
> after you finish extracting the axioms that usefully
> summarize a wide range of experience. But this is
> not the natural order for discovering the axioms.
>
> Or maybe axioms are the cart and experiences are the cartload.
> It can a take a couple hundred or a couple thousand years of
> experience with a motley crue of crude examples before some
> people will start to notice that the same darn patterns of
> thought tend to keep turning up in what appears to be the
> darndest places, and the useful sorts of axioms only but
> gradually percolate themselves to the top of the heap.
> But even this is a retrospective illusion. At the
> beginning of the story you don't even know what
> the "examples" are supposed to be examples of.
>
> This is the way that it has been with all the best axiom sets that I
> know,
> like those that define graphs, groups, and other mathematical materials.
> Now, once you abstract a useful set of axioms, it is possible to engage
> in a certain amount of free variation with them, and it is possible to
> hit on some lucky finds that way, but this sort of "luck" all depends
> on the mega-years of perspiration that went into finding the initial
> set of principles.
>
> It is necessary to think about abstract structures as independent spaces,
> formal or mathematical models that are "models" in one sense because they
> are defined by axioms, but "models" in another sense because they analogue
> an aspect of real experience.
>
> But these models can at best be approximations to reality, and so there is
> an unavoidable risk in using them, not that there is an alternative for us!
> The act of creating or discovering a model is what is known as "abductive"
> reasoning. It becomes necessary to distinguish "thinking within the model" --
> thinking inside the box, if you will -- from "thinking of/about the model",
> all the sorts of reasoning of that it takes to come up with the axioms in
> the first place, and all the sorts of reasoning that it takes to evaluate
> the utility of the corresponding model for any exterior/ulterior purpose.
>
> But the catch is this: Thinking within the model can be done by
> deductive reasoning, and maybe supported someday by the ilks of
> theorem-provers that we all know and love, but thinking up the
> model to start with, and testing the model in the final analysis,
> except for mere logical consistency, just cannot be covered by
> deductive means alone.
>
> This is something that will just have to be taken into account
> in designing the logical architecture of ontology using systems.
>
> Jon Awbrey
>
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>
> John F. Sowa wrote:
> >
> > Rich,
> >
> > JS> The axioms get in the way.
> >
> > RC> Does that mean 'The (top level) axioms get in the way'?
> > >
> > > If so, then the top level is the empty level, as you suggested
> > > earlier. And any conceivable context of objects, properties
> > > and axioms could be the next level below the empty top level?
> >
> > The top node is true of everything. Therefore, the only axioms
> > that are associated with it are the tautologies. They can't
> > get in the way of anything.
> >
> > The organization of any hierarchy is determined by the dependencies
> > between nodes: category X is beneath category Y iff the existence
> > of something of type X implies that it is also of type Y. Any
> > category that has no such dependencies is could be placed at a
> > level immediately beneath the top. The analysis of the
> > dependencies determines the hierarchy.
> >
> > John
>
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