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Re: [ontolog-forum] Visual Complexity

To: Patrick Durusau <patrick@xxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Tue, 6 Feb 2007 09:43:26 -0600
Message-id: <p06230902c1ee49a18f38@[]>
>A rather truncated reply on two of your points:
>Pat Hayes wrote:
>>Highly snipped reply, still long though :-)
>>>>>An ontology is first formed at conceptual level (design)  being
>>>>>inmplemented is the last step.
>>>>What do you mean by "implemented"?
>>>I mean that the LOGICAL THEORY does not have a 
>>>single  language attached to it
>>>You can express a logica theory using a language, but the theory IS NOT
>>>the language.
>>The theory is not the language, but it is (and now I am quoting an
>>almost universally accepted technical usage of 'logical theory') a
>>set of sentences in some formal language. So any such logical theory
>>has a single language associated with it, to wit, the formal language
>>it is written in. So the idea of a theory which is somehow
>>independent of a formal language, is (literally) meaningless. If you
>>mean something else by "logical theory", it would help if you could
>>explain what you mean.
>I think the point was the superclass/subclass and a relationship between
>the two is independent of the language in which those are expressed.    (01)

Well, if sub/superclass is ALL that is being 
talked about, then indeed that very simple idea 
can perhaps be treated as so common to so many 
languages that it might be treated as 
language-independent. But even there, there are 
in fact subtle differences in meaning between 
languages. For example, OWL requires that 
subclass means exactly subset, whereas RDFS 
allows two coextensive sets to have a subclass 
relationship. This may seem to be splitting 
hairs, but in fact this difference has many 
consequences: for example, with the OWL view, the 
classes of human beings and bipedal arthropods 
without body hair (which happen to have the same 
members) must be the same class, and there can 
only be one 'empty' class (with no elements), 
neither of which apply to RDFS. Again, in many 
systems, a class cannot be an element of itself, 
so finding such a 'membership loop' signals an 
error of some kind; in RDFS such loops are 
possible and actively used in reasoning.    (02)

>If that is not the case, then there can't be any mapping between formal
>languages    (03)

Not at all. It means only that the mappings get 
more complicated to state. For mappings from RDFS 
and OWL into CL, see papers by Chris Menzel and 
http://philebus.tamu.edu/cmenzel/Papers/AxiomaticSemantics.pdf    (04)

BTW, the recent IKRIS project (see 
http://nrrc.mitre.org/NRRC/ikris.htm ) was 
entirely devoted to defining mappings between a 
number of very different and very expressive 
formal languages, in enough detail to allow 
machine translations between them.    (05)

>and perhaps the "my ontology first and last" crowd has a
>point. If we don't simply all use the same one, then integration is
>simply not possible. Reasoning that if we can't go beyond the formal
>language, there is no basis for comparison.    (06)

The basis for comparison is the semantics: 
formally, the model theories. That (or some 
equivalent mechanism) is how precise comparisons 
between ontology languages must be made. Just 
rendering the intended meaning in rather loose 
English is not a sufficient basis for writing 
translators.    (07)

>But, if you accept the notion that languages, formal and otherwise,
>contain representatives that are not co-extensive with the subjects they
>represented    (08)

...? Of course I accept that, if I understand it. 
It sounds like a restating of Korzybski's 
doctrine that the map is not the territory (??) 
And of course it is borne out by the formal 
semantics, which also distinguishes between the 
language and what it denotes.    (09)

>, then integration is possible (I won't say likely or easy).
>>>>But my point is that any particular ontology is
>>>>going to be represented in SOMETHING: it might be
>>>>OWL or CL or GOFOL or Prolog or RDF or Concept
>  >>>Graphs or CGIF or who knows what. But it can't be
>>>>represented in nothing, and it can't be
>>>>represented in some kind of supervening
>>>>?bernotation, because there is no such universal
>>>my point is that knowledge in any domain is 
>>>first represented by concepts and
>>Not always. While this may be true for many cases, there is a great
>>deal of knowledge which is necessary for use by reasoners but is
>>rarely put into words in NL, because all adult human speakers already
>>know it, so they never have to say it to one another. And there are
>>distinctions which are central to ontology engineering decisions
>>which are almost never put into words, except by rather obscure
>You may have a point that ontologists skip over what they assume is
>universal knowledge or assumptions and therein lies part of the
>difficulty in integrating ontologies, particularly since they can't see
>beyond their formal languages, cf. your earlier point.    (010)

No, you misunderstand me. Ontologists don't skip 
over this stuff. They are obliged in fact to 
wrestle with it. Cyc consists of little else, 
millions of such 'facts'. My point is that 
looking at the words people use is of little help 
in getting this common-sense stuff formalized, 
since people rarely use NL words to talk about it 
(and when they do, the words usually hide, rather 
than reveal, the true ontological structure. As 
an example, look at the multiple uses of spatial 
prepositions like "on" in English. Cyc is obliged 
to distinguish around ten different senses of the 
meaning of "cover".)    (011)

Your phrasing "see beyond their formal languages" 
is revealing. If you think that the use of a 
formal language restricts ones imaginative scope 
in describing the world, I suggest to take a look 
http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=5493    (012)

>BTW, I am intrigued that here you make the rather remarkable claim
>about  "...all adult human speakers already know it...." and yet deride
>a similar claim below with reference to "common sense knowledge."    (013)

It is the same point. We all have this knowledge 
(in some sense: we act upon it) but we rarely, if 
ever, articulate it: and it is extremely hard to 
make it explicit for machines to use (ie put it 
into an ontology). So the mere possession of 
unarticulated pre-formalized knowledge is no 
guarantee that this knowledge can be formalized 
easily.    (014)

>>>, and knowledge representation shold be
>>>as as independent as possble from formalisms to be widely usable
>>Well, we really do disagree about this. First, I don't even accept
>>that KR without formalism is really worth being called KR. Second, I
>>don't think unformalized knowledge is actually much use in building
>>ontologies. So-called "common sense' knowledge is supposed to be
>>universally shared among competent adult human beings, but even if
>>that is true, it has not been of much use in the task of formalizing
>>it. And third, I don't think it is even meaningful to speak of
>>representing knowledge independently of any formalism or notation for
>>representing it. That is, unrepresented representation is an oxymoron.
>I think you are reading the original post too narrowly. Sure, to speak
>of representation is to presume some notation, no doubt about that. But,
>should the notation be confused with what it purports to represent?    (015)

No, of course not. And nobody makes such a confusion.    (016)

>I think the original post meant to refer to how the same subject could
>in fact be represented by any number of notations.    (017)

That is of course true. But that is not what the 
post said: what it said was that the ontology 
should *represent* its content in a way that was 
independent of the particular notation. Which is 
impossible: since by representing it at all, one 
must choose a notation to represent it in.    (018)

>Unless, of course, you wish to deny that superclass/subclass in SUMO is
>the same as superclass/subclass in OWL or CYC or some other logical
>notation    (019)

They probably do differ slightly in meaning, see above.    (020)

>because it is "meaningless" to try to look beyond those formal
>languages.    (021)

No, I do not claim that. However, I do think that 
formalizing ones intuitions is a very good way to 
sharpen their meaning; and I know that one often 
finds hidden weaknesses or gaps in the intuitions 
when one does this as an exercise.    (022)

>From a topic maps perspective, if you say they are "same as"
>then there was some basis on which you made that assessment. Why not
>simply make that explicit?    (023)

Well, I would like to hear more about what counts 
as a 'basis' here. If every claim must have a 
basis, we seem to be in an infinite regress.    (024)

>Hope you are having a great day!    (025)

And you.    (026)

Pat    (027)

>Patrick Durusau
>Chair, V1 - Text Processing: Office and Publishing Systems Interface
>Co-Editor, ISO 13250, Topic Maps -- Reference Model
>Member, Text Encoding Initiative Board of Directors, 2003-2005
>Topic Maps: Human, not artificial, intelligence at work!
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>    (028)

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