Sam
That thread is beginning to be very difficult to follow-up for everybody I'm afraid.
I suggest to try and split it into specific issues.
For the moment I've tried to put something "readable" on-line in a few slides at
http://www.universimmedia.com/topicmaps/hypergraph/
To meet your concern about any mix-up of the model and its interpretation,
I've put every topic map term and any reference to "semantic" out of the mathematical
model terminology.
Please Patrice and Pascal correct me if you find something wrong or misleading in those
slides.
The second part - topic map interpretation is "to be delivered".
More tomorrow :))
Bernard
----- Message d'origine -----
De : "Sam Hunting" <sam_hunting@yahoo.com>
À : "Bernard Vatant" <bernard.vatant@mondeca.com>; <shunting@etopicality.com>; "Topic Map
Mail" <topicmapmail@infoloom.com>
Cc : "Pascal Auillans" <pascal.auillans@mondeca.com>; "Patrice Ossona de Mendez"
<pom@ehess.fr>
Envoyé : mercredi 20 février 2002 19:15
Objet : Re: Consistency and Formal Model Re: [topicmapmail] Can a resourceRef be a topic
> [sam]
> > > [1] "A formal model is needed" does not mean "a formal model is
> > > needed ... This or any model must be justified in terms of the
> topic
> > > map paradigm, not the other way round. If it doesn't meet that
> > > criterion, another formal model may always be chosen.
> >
> > I understand your point. But the "terms of the topic map paradigm"
> > will remain fuzzy and lead to endless debate until they are expressed
>
> > in *some* formal model that will anyway make some cutting choices on
> > critical issues, if it has to be formally consistent. This
> > model must of course be agreed upon by those who legifer on the
> > specification, that is ISO/IEC JTC1/SC34. And I completely agree that
> > it could be *any* model, as far as it is formal, internally
> > consistent, and agreed upon.
>
> I vehemently agree with what I see as the intent of what you say here.
> And the opportunity costs of endless debate are huge. The pot of gold
> at the end of this mathematical rainbow is, as I see it, to ground the
> topic map world as firmly in a formalism as the relational world is.
> (And math is the right formalism.) But as Elaine Svenonius says,
> "objectives determine ontology," objectives are part of the paradigm,
> and the objectives will, for good or ill, be as fuzzy as the humans who
> share them are.
>
> [sam]
> > > [2] The mathematical model, being purely formal, describes a topic
> > > map using purely mathematical constructs. Math has no notion, and
> > > can have no notion, of anything that we would call "semantic
> > > inconsistency" (where "semantics" includes meaning as humans
> > > understand it.)
>
> [bernard]
> > Let me try to make it clear again in what sense I use "semantic
> > consistency" in that context. It has somehow to do with human
> > interpretation to begin with, but it can be checked by the
> > model in a formal way. It is a two-stage process:
> >
> > 1. Declare that "out there subjects" (in every sense of the topic map
> > definition) are correctly represented by model objects (including
> > relations), and that such type of subjects is represented by such
> type
> > of objects etc. That is the "agreement on the choice of a model" -
> the
> > typical work of a standard specification.
>
> Hmmm... I can't parse this. Topics can be typed, but I don't see how
> "out there subjects" can be typed, in themselves, as opposed to being
> typed in the model. And I don't know what model objects are either, and
> whether they can be subjects. Sorry. (I guess this is an illustration
> of why math is more clear ;-)
>
> [bernard]
> > 2. Respect afterwards the rules and constraints of the agreed-upon
> > model, and accept that what is non consistent (mathematically
> > speaking) with those rules and constraints is non conform to the
> > model.
>
> Sure. And if topic maps are to be a neutral envelope for the knowledge
> interchange, then it would seem a good rule of thumb to put as few
> constraints as possible in the topic map model, as opposed to
> applications of that model. It's a lot easier to add constraints to the
> model than it is to take them out later, once they have been added.
>
> [natural language example deleted as potential source of endless
> argument ;-)]
>
> [bernard]
> > The model will not declare which of the assertions is/are right or
> > wrong, if any. It will simply say that the set is not
> > consistent. That is an example of what I call "checking semantic
> > inconsistency"
>
> But in the topic map model there is no way to assert right and wrong in
> any case. So I don't understand the shift in language from
> "mathematical consistency" to "semantic consistency." Though see below.
>
> [bernard]
> > To go back to the example that started the thread: It seems conform
> > to all current rules of knowledge representation that individual
> > objects and universal classes (types) are separate generic types. If
> > Sam Hunting is declared as an individual object, it should not
> ^^ "he",
> thank you very much ;-)
>
> > be used as a type. The model has to allow the implementation and
> > checking of such rules.
> >
> > If I add "semantic" to "inconsistency", it's because the model I have
> > in mind deals with semantic layers, and one fundamental constraint is
> > that an element can't belong to two layers at the same time - which
> is
> > the same kind of constraint that forbiding a loop in a class-subclass
> > relationship.
>
> That is the heart of the issue, I agree. But I disagree about "can't"
> belong. "shouldn't", perhaps -- according to a point of view -- but
> can't? For example, the subject that is the person Bernard Vatant might
> simultaneously be an instance of what it means to be human, and the
> typification of the Boy Scout virtues (kindly, brave, reverent...) . [I
> was going to use myself as the example here, but there are people on
> the list who know me.]
>
> [bernard]
> > There again, maths can't tell you what the semantic layers *are*. But
> > once you've agreed upon the fact that there are such things as
> > distinct semantic layers, you have to choose for each object to which
> > layer it belongs, and keep consistent afterwards.
>
> If I can keep straight the semantics for *any given* choice of
> layering, why cannot multiple choices be made? (If the answer is, "the
> formalism," see the discussion at [1] above.)
>
> [sam]
> > > "Frobnostification," for example, could replace "semantic
> > > inconsistency" with no loss of formal precision -- both are a
> > > "prose add-on"s to the formalism, and no more or less formal than
> > > the prose of any standard or specification.
>
> [bernard]
> > I disagree. As I told you a few days ago in a more private forum,
> > "Frobnostification" could replace any term used inside the model to
> > name objects and relations. But "semantic consistency" has something
> > to do with the way you use the model. It's different, it's not
> > inside the model. Of course you can call things as you like. Language
> > is a moving place, but ... somehow we communicate, eventually ;-)
>
> I think we do agree. I say frobnostification is a prose add-on to the
> formalism, you say it's not inside the model, it has to do with the way
> you use the model. Agreed that lanuage is a disputed terrain, of
> course.
>
> [sam]
> > > "Frobnostification," in fact, would be more precise than "semantic
> > > inconsistency" in that it would avoid introducing an implicit
> > > functional specification into a formal model.
>
> [bernard]
> > Wrong. It's not a functional specification of this particular model.
>
> Right! (I mean, it's not right that I'm wrong, it's wrong that you're
> right). What I mean is that you have a certain, reasoned view about
> what it is reasonable or meaningful for a given topic map to assert.
> These are objectives, outside the model. But the language transition
> "semantic consistency" (outside the model) to "semantic lift" (inside
> the model) suggests to me that indeed the objectives if not actually
> implicit in, can be read into, the model. A disputed terrain...
>
> [bernard]
> > Consistency is a basic rule for the use of *any* model. In physics,
> > it has a variant called *experimental falsification*.
> > And a good model is a model that can be falsified ...
>
> Not right. Maybe right if you're Karl Popper, but not right if you're
> Ludwig Wittgenstein. (And the topic map paradigm, being a neutral
> envelope, has to be capacious enough to accommodate *both*
> philosophies.) Not all human knowledge, and certainly not all knowledge
> that people will wish to interchnage, is falsifiable. Certainly TBL
> believes this.
>
> [sam]
> > > That is, the label "inconsistent" is used to deprecate or forbid
> > > certain results of the intersection of *this* formalism with
> > > certain applications of the topic map paradigm.
>
> [bernard]
> > Yes. I assume that completely. Because I really think that without
> > formal model, you can interpret topic map paradigm to produce junk
> > topic maps.
>
> But Bernard! There are all kinds of unexamined assumptions here. First,
> you shift the argument (I think, there's no article) from "a formal
> model" to "this formal model." Then shift to a notion of consistency
> that depends on the idea that only that which is falsifiable is
> interchangeable. Then shift to the idea of "junk" topic maps. I don't
> know what "junk" means, but (a) I do know that attempts to legislate
> good practice have consistently failed (the Academie des Topic Maps?
> ;-) and (b) what you may consider "junk" may well have value to someone
> else.
>
> [bernard]
> > If you want to keep the paradigm completely open, because
> > you don't want to legifer on what is junk and what is not, say
> > that the model will define topic maps conformant to it, as a subclass
> > of more generic objects. As a matter of fact, if you look closely at
> > the model, you will see that it allows itself different subclasses
> > (for example stratified or not).
>
> OK -- I'm missing this part. It may be that there is a way for us to be
> in vehement agreement here as well.
>
> > > 3. "Semantic stovepipes" is my label for the danger I see in the
> > > implicit functional specification of "frobnostification" in the
> > > documentation for the formal model.
>
> [sam]
> > > The danger is that the very sort of knowledge interchange that
> > > topic maps should be encouraging will be decreased ("islands of
> > > markup" all over again).
> >
> > Ha! *Global* knowledge interchange, that is? For myself, I prefer to
> > get islands of communication inside the shores of which I know that
> > understanding tands upon common definition of terms, that an ocean of
>
> > so-called interoperability where people just believe they agree, when
> > speaking of completely different things with the
> > same apparent language.
>
> Well, Bernard, there are only islands because there is an ocean! And
> yes, any two islands will have topics that are "false friends" in
> addition to those that are "true friends." As usual, it's a matter of
> satisficing (Simon) rather than perfection....
>
> [bernard]
> > Agreement based on contradictory interpretations of the same document
> > is worse than acknowledged disagreement which leads to further
> > discussion.
>
> Debatable, and certainly application dependent. This could be true for
> any given relation and yet the net result be positive for a topic map
> considered as a whole. (This is why, in my view, these agreements need
> to be expressed contractually, but that is another thread altogether.)
>
> > For example, a very interesting consequence of the model,
> > is that you will be able to check if two maps have declared semantic
> > layers consistent with each other, before merging, and if not, be
> > aware that this merging will certainly not make sense, even if
> > syntactically possible. And send that back to both authors, pointing
> > to where they disagree, and that if they really want to interoperate,
> > they have to do something about it.
>
> This is surely a consequence of any formal model?
>
> > > Of course, "in danger, opportunity." It may be that what Bernard
> > > and his team of mathematicians have come up with is a way to
> define
> > > what a "topic map application" is, which would be a fantastic
> > > result.
> >
> > I'm not sure what you mean by a "topic map application" there.
>
> This was a vague thought -- could two maps without "mismatch" be
> regarded as the same topic map application? (I use mismatch as a more
> neutral word than "consistent", and suggesting impedance mismatch.)
>
> > And just a precision. It's not *my* team by any means, just a team
> > that happened to delegate me as a go-between with the dangerous
> > outside world.
>
> Sorry -- I meant more "the team whose results you have presented to
> us." As to "danger", I meant danger to the topic map paradigm, which is
> what is important.
>
> S.
>
>
> =====
> <!-- Topic map consulting: www.etopicality.com
> Open source topic map toolkit: www.goose-works.org
>
> "A human is a topic map's way of making another topic map."
>
> -->
>
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