With respect to ontologies, I would consider two ontologies isagelous
if they can be translated into each other, resulting in no loss of information
and no addition of information in any one translation step: a round-trip translation
would result in exactly the same ontology, syntactically and logically, though
the order of the elements in any *list* does not have to be identical,
if it makes no difference to the logic. The round-tripped ontology would
have to generate the same inferences from the same data. The information could,
in one form (say, an if-then rule in text form in OWL), be in a formatted text,
while in another form (e.g. CL) it could be in rules executable by a
CL-conformant reasoner. I would consider the translation to be lossless if
the same elements are created after a round trip. It would be the task of
the translator program to be sure that there is no loss or addition of information.
I imagine that it might be difficult to prove
mathematically that two ontologies in the same format (say the original and a
round-tripped version) are in fact the same. I don’t know enough
about “normal forms” to know if or how this could be proved.
An operational test with a suite of test data or problems might at least
provide some probabilistic assurance that they are the same. Perhaps the
translator could be structured to create its own normal form in any given
format, and in that case perhaps translating any two ontologies into the same
format might be able to prove that the original two are isagelous (perhaps if
one is concerned only with the logical structure, one might ignore comments and
the actual labels? In this case the labels for the data to be processed would
have to be translated as well)
As you can see, I haven’t tried to formalize
this notion of “isagelous” wrt ontologies, though I suspect that
some notion of “same information” is meaningful there too. I
suspect that there is some (a lot?) of work along this line of which I am utterly
ignorant.
Pat
Patrick Cassidy
MICRA, Inc.
908-561-3416
cell: 908-565-4053
cassidy@xxxxxxxxx
From: Pat Hayes
[mailto:phayes@xxxxxxx]
Sent: Friday, February 06, 2009 5:01 PM
To: [ontolog-forum] ; Patrick Cassidy
Subject: Re: [ontolog-forum] RDF & RDFS (was... Is there something I
missed?)
On Feb 6, 2009, at 3:46 PM, Patrick Cassidy wrote:
I had occasion, years back when I was doing DNA
research, to coin a term “isagelous” to refer to abstract
informational objects that have the same information content, but in different
physical or syntactic form. It is from Greek, “iso”
meaning “same” and “agelos” meaning
“information”. It can apply to a sequence of DNA and its
corresponding RNA transcript, or to a file and its compressed version, or to a
message and its encrypted form. It also might be applied to different
implementations of the same algorithm in different computer languages, if there
are no functional differences.
Thus – “they are isagelous
implementations of the same algorithm”
Useful word, to be sure. I notice though that in your
example you still have to say "algorithm". So transcribe this to
ontologies, where we might have isagelous formalizations, in CL and OWL-2, of
the same.... what?
PS is it pronounced i-SA-gelous or isa-GEL-ous?
On Feb 6, 2009, at 1:28 AM, Matthew
West wrote:
PS - I'm not sure about
where this idea of a mental model of an ontology
came from. I never mentioned it, and I certainly don't have an ontology in
my head. Of course the ontology has to be represented in some way - CL,
RDFS, OWL, UML, EXPRESS, arse-barcodes, who cares ?
What is this thing that
is in common between al these different file formats? Where is it, if not in
your head? This is rather like the old chestnut of saying what exactly a
program is, if you can write the 'same' program in several wildly different
programming languages. For example, quicksort can be implemented in just about
any programming language, and its still quicksort. In CS we have the useful
distinction between algorithm and program, maybe we need a similar
terminological distinction for ontologies. Any suggestions?
[MW] Ok. So is the quicksort program in
your head the same as the quicksort program in my head (I even remember writing
one once in Basic)? Talking about what is in someone’s head just
doesn’t cut it I’m afraid. It is at best a loose way of talking.
Speaking as a card-carrying
cognitive scientist, I have to disagree. We have to be taking intuitions
seriously here. They are our prime, perhaps our only, source of guidance when
writing formal theories.
I think that fear of talking about
intuitions is a residue of the intellectual blight caused by behaviorist
psychology. Ironically, behaviorism has been a rejected methodology in
psychology for about 30 years now, but the news of its demise seems not to have
reached everywhere else yet.
Where you have several things that have
something in common, what you do have is an abstraction, and my extensional
analysis would make that a class.
Fine, but that says nothing. Any
set of things is a class: but a class containing, say, a C++ implementaiton of
Quicksort and a LISP implementation of a parser, isn't any kind of algorithmic
abstraction. What makes some classes useful is that their instances have
something in common: and that thing that they have in common has to be more
than just being in the same class, to avoid circularity.
So if I have 5 copies of the same content
There, that will do. Its the content that they have in common.
, there is a class that represents the
pattern
or is the pattern? See my point?
Its impossible to avoid talking of this thing-in-common, whatever it is. Maybe
we should face up to this need, and agree on a common terminology.
that is common to those 5 files. And if I
have the “same” ontology that is represented in different
languages, then there is a class that represents that sameness.
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