Tuesday, December 20, 2005
Lattice of ontologies
Function/structure descriptions
From the Protégé OWL forum discussion
This
discussion goes back several beads and is most excellent
Paul
Prueitt is using foot notes to make comments and
then
in the next bead he elaborates on these footnotes à [327]
Continuing communications from Andrea Proli
Paul
Well, don't worry I'm not offended at all, I'm just trying to integrate my own vision with a conflicting one, and thus make my vision more generalized, and better if possible. But still, this requires some kind of negotiation and hard dialogue so please forgive me if I am too strict and/or offending in my way of thinking. So, you say: [1]
You said:
"the inflexibility itself comes from the foundational issues that Church, Turing and Godel addressed - and these have to do with representation of completeness of description and consistency over logical inferences."
I think some history is needed here. Information, computability and complexity theory are not simply connected to mathematics, but are logical consequences of how mathematics was conceived after Gauss formalized non-Euclidean geometries. Before that, mathematics was about universal, logical "truths".
After that, when it was clear that neither the classical nor the non-Euclidean geometries was "right" or "wrong", but simply was founded upon different assumptions, mathematics became about logical consequences of axioms which was taken for granted, without any universal "truth" being studied. And that motivated the study of theory axiomatization and of formal properties of those theories: mainly, whether theorem proving could be made a mechanical task, and whether every theory could have in principle been axiomatized. [2]
Then comes Goedel (sometimes spelled Godel) . Goedel was a philosopher and his work was about mathematics and logics: his incompleteness theorem has been deemed to be the most important scientific result of the last century in mathematics (not CS). Those results showed for the first time that not all theories are finitely axiomatizable, and this is why it makes sense to talk about "computability", "computational complexity", "completeness", "soundness" and so on. [3]
That was the start of information theory, computability theory and complexity theory.
Because of that, I don't think those foundations are more inflexible as logics and mathematics are, and correct sciences must commit to the language of logics and mathematics for unambiguously communicating formal statements and correctly reasoning about them. [4]
Because of this, I can't see a way to go on without these foundations or to modify them and make them more "flexible", as they are a single whole with mathematics and logics, and science eventually commits to mathematics and logics, full stop.
Paul said
"the problem is that the other communities (like the medical community) is forced to accept what ever is created"
I don't know, but I suspect (really, I'm asking you) if you mean that we are lacking flexibility in accomplishing the needs of disciplines that are not founded on mathematics and logics. [5]
(note
Paul edited here to separate concepts)
These disciplines still need some way to represent knowledge and reason about it (is this what you mean when you refer to linguistics and medicine, and "natural" science?). Again, this is nonsensical, if (“if” is inserted by Paul) we can't be "flexible" in that, they should not rely on services that are the concrete reification of theories they don't agree with.
By the way, if we accept the foundations and the overall logic-based approach, the problem of satisfying user requirements is still fundamental and it is important to bring it into this community. End users are entitled to tell what requirements they want to be fulfilled, so what the medical or linguistic community exactly want?
Are they only asking for different/new functionalities, or are they arguing that things should be done in a different way? [6]If so, do they have any knowledge on how this should be done? Do they manage with software companies, who require solutions to be standard, reliable, and quickly delivered? In any case, I think it would be very helpful to have a wish list from medical scientists, lawyers, and whatever else community who needs concrete help in solving those problem which involve knowledge representation and reasoning tasks, but i'm skeptical about the existence of a different approach to their fulfillment different from the one currently undertaken by W3C and the CS community in general. [7]
You said:
"As to the relevance to this notion of natural complexity, the anonymous individual is one way to put a symbol in place that can allow a late binding of the meaning to be given that symbol. right?"
Right, what I don't understand is what you are claiming about them: are they good or bad (bad, I suppose...)? and if they are bad, how would you replace them? would you simply drop them, or give them a more proper name? what semantics would they have? and so on...
Again, please forgive me if I turn out to be offending in any way, it's a hot discussion as you probably guess ;))
Cheers,
Andrea
[1] So that I can catch the relevant points I am going to use foot notes and then expand my comments [327]
[2] There was also in the time immediately after Godel some growing interest in the notion that formalization was itself subject to critic. I do not know this history, as it is not one that is easily accessable, but clearly the distinction made in the literature about the early Wittgenstein (1905 – 1917?) and the later Wittgenstein is pointing to a failure of formalism to be as “expressive” as natural language. One reason why I dislike the use of the notion of logical expressiveness in the OWL community is that the word is stolen from another connotation.
Logic is NOT expressive of the natural phenomenon. But one can not say this in the computer science community, because “they” own the word “expressive”.
The same polemic occurs with the use of the phrase “computational complexity” and formal semantics”. This phrase already makes a claim that many do not agree with. See Judith Rosen’s discussion at [314]
[3] The way these things are talked about in some literatures, specifically those of Tarski and thousands of individuals with similar thinking, is not the same as how N Rashensky and R Rosen and others talked about these things. But this logic school, which I will associate with the AI school, made claims that they were the only ones addressing the post Godel world.
John Sowa and many others are still doing this. I have called this a form of fundamentalism simply because the school (including the work we referenced by Ian) uses natural language in a way that is simply (from my point of view) incorrect. I do not mind their use of technical terms if they are not authoritarian (as James Hendler certain is). They however, will not acknowledge the issues that are raised and pretend as if there is no legitimacy to the issue of degeneracy in metabolic signal pathway modeling as pointed out by G. Edelman, for example).
So , because they, Hendler and group, have controlled funding peer review, there is no alternative to the mainstream. The situation borders on fraud because they monopolize government funding and makes relationships with business so that certain status quo continue to produce almost utter non-sense as our foundations to information science. (see: http://www.ontologystream.com/area2/KSF/KnowledgeScience.htm) as an example of grant proposals where Hendler, and his students, served as peer review and caused the grant to not be awarded.
[4] The point is that IF there is a problem is creating precise and correct logical theories about natural processes such as human thinking, as I Prigogine points out in “End of Certainly”, then one cannot continue to impose on natural science the imposition that are imposed by this school of logic and by the mainstream of computer science. Yes?
Is this school of logic very similar to a religion? I say yes.
One has to look for something different, such as notion of “open” logic, or quasi axiomatic theory (Victor Finn): Finn, Victor (1991). Plausible Inferences and Reliable Reasoning. Journal of Soviet Mathematics, Plenum Publ. Cor. Vol. 56, N1 pp. 2201-2248
[5] It is precisely this point that I, and others, am making. There are alternatives, and suggestions as to what do to in the case that medicine and other life sciences cannot be founded on classical logics. But unless the Emperors of Logic (to steal a phrase from Roger Penrose), acknowledge the complete and total incomprehensiveness of what is not done in the OWL inference engines, then we cannot start on developing these alternatives.
[6] The argument is that information science must acknowledge the limitations to classical logic and quit an endless Zeno’s paradox. Our society must have good information science now, and it can not get it as long as the mainstream computer scientist is pretending as if things like 13 year development project to visualize and edit RDF / OWL is acceptable, or the two decade funding of Doug Lenat, or the four decades of massive AI funding.
[7] Why are you skeptical?