At the risk of further wasting everyone's time, I would point out that
"being clear about the intended interpretation" depends on there being
a common base level of understanding.
For SWIFT, the international banking community has over the years
hammered out some very clear definitions of expected practice and their
relationships to the exchange of funds. Yes, there is a new kind of
instrument every 3 months, and yes, there are subtle differences in
practice and ways to maximize benefit that come from carefully
analyzing the behaviors of others, but overall, the basic financial
transactions and practices are well-established in significant detail.
Finance is pure artifice: all of the elements are controllable, except
for the behaviors of individual agents. In finance, the theory is the
basis for the discipline.
Health care, OTOH, is not a controlled artifice. It is people
discovering and reacting to nature. It is a set of diverse practices
with overlapping groupings and terminologies, some parts of which are
based on long-established practices and models of the human body and
disease, and some parts of which are based on 'cutting edge research'.
'diagnosis' is about identifying a set of symptoms and reasoning as to
the most likely 'theoretical' explanation for the cause, and
'treatment' is about mechanisms and practices that are statistically
effective in attacking the presumed cause. So what you have is a
language in which there is only general agreement on the meanings of
terms or the conclusions to be drawn from reported observations. Even
the reported observations suffer from the difference between perception
and conceptualization -- what is reported is not what happened, but
rather what the observer thought happened, or not what all happened,
but only what the observer measured.
You can only engineer common knowledge to the extent that it is
common. And the difference between "common knowledge" and "reality" in
the natural sciences can be quite important. So William is absolutely
right -- scientific ontologies are a lot harder than geometry.
Percival Lowell convinced us that Pluto was a planet, but now it isn't,
and volcanism was explained by tectonic plate motion, except for hot
spots, and people are in some ways more like pigs than apes. Medical
science and medical practice are probably in the worst upheaval of any
scientific endeavour. So it should not be surprising that it is
difficult to codify our "knowledge" in that area, or at least difficult
to codify it well enough to be currently useful.
A problem we have not discussed is the one I think of as 'factorization
of the problem space', and it is characteristic of medical ontologies.
The problem is that some viewpoints produce models of the world that
are hard to relate to other models, because they have nearly no common
basis. The simple example I have used from manufacturing is the
portable hand drill. The design engineer sees a system composed of an
'end-effector' (the chuck and the cutting tool), a motor and drive
shaft, a control system (the trigger, speed controls), a power supply,
and a housing. Each of these is then decomposed into its elementary
parts. The assembly engineer sees a two-part housing, of which one
part is mounted on the conveyor in a specially made fixture. Then he
looks at the list of all the parts and chooses the ones that go on the
'bottom' of the fixtured housing part, then the ones that go on top of
them, etc., until the last assembly step of putting the 'top' housing
on the whole thing and tightening the fasteners. There is nearly no
relationship between the assembly model and the subsystem model, and
their descriptions of any architecture above the elementary parts will
have no cognates. The terminologies cannot be translated between the
viewpoint models. The design engineer relates parts to functions; the
assembly engineer relates parts to handling actions. And yet, these
ontologies are for an engineering artefact -- our knowledge of them is
'complete', except for variations in part quality and process
execution. How much more difficult must this problem become when you
don't control the problem space being modeled?
-Ed
--
Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 Cel: +1 240-672-5800
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority."
Matthew West wrote:
Dear
William,
I
think there is an answer to your question:
The point
remains, which was the point of the mail: ontologies do not guarantee
complete "interoperability", but that term probably needs and does not
have a definition. And if ontologies only guarantee something partial,
what is it that they DO guarantee? And why, in practice, do even
primitive but logical shared messaging specifications like the early
tagged syntax S.W.I.F.T provide so much value, and not seem to lead us
into trouble. (While some shared but literally insane messaging
specification like the health care EDI messages create huge error and
correspondingly huge employment opportunities
I
think the key is being clear about the intended interpretation/model,
and making sure you make a distinction when the intended interpretation
is actually different (inconsistent).
Logic
does not have all the answers here.
Regards
Matthew
West
Information
Junction
Tel:
+44 1489 880185
Mobile: +44 750 3385279
Skype: dr.matthew.west
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On Thu, Mar 8, 2012 at 1:32 PM, Christopher
Menzel <cmenzel@xxxxxxxx> wrote:
Am Mar 8, 2012 um 6:23 PM schrieb William Frank:
> I think is the essence of this point is:
>
> "The number of possible conflicts is infinite, and no fixed set
> of universal definitions can anticipate and rule out all of them."
>
> This is true of *logical necessity*; so it is something that we
always live with
>
> The reason for this truth is that
>
> there is no guarantee that all the models for
> any theory G are consistent with one another.
I not sure what you and John mean by that -- consistency is a property
of theories or, more generally, sets of sentences. It doesn't make any
clear sense that I can see to say that two models are inconsistent. I
suppose we can make something up, e.g., models M1 and M2 of theory G
are inconsistent with each other if there is some sentence A in the
language of G (obviously not a theorem of G) to which M1 and M2 assign
different truth values.
Actually, I was making something up to save words, that seemed clear,
indeed only theories can be consistent or otherwise, two models are
inconsistent if there are two theories of which they are models, which
are inconsistent.
> More strongly, unless the theory G is complete, which no theory as
expressed in an application will be
It's not obvious to me that that is so. There are well-known examples
of complete first-order theories (e.g., the first-order real number
theory and Euclidean geometry both have complete axiomatizations). Such
theories obviously cannot contain a lot of arithmetic, but it's not
obvious that an interesting practical ontology has to contain the
arithmetic needed to guarantee incompleteness and hence can't be
complete.
Well, what I had in mind is ontologies for things like trade services
or pharmaceuticals. These seem alot more complex to me than geometry
etc. As many in these exchanges have noted, most large software
collections are probably inconsistent, but consistency is to be hoped
for. To expect one of them to be complete is a stretch, and probably
not desireable.
> (only theories as bounded and richly
expressed as second order arithmetic tend to be complete),
Eh? There is no complete axiomatization of second-order arithmetic.
Sorry, I was not clear. There
are two meanings of complete floating around. I was using semantic
completeness, in the model theory semantically complete sense, as used
by Baldwin "what is a complete theory?"
"
A (consistent) theory T in a logic L is complete if for every
L-sentence ,
T |= L
or
T |= ¬ L.
"
where the sideways sleepy |= means logically follows from, not is
provable from.
As opposed to the completeness of a proof theory, which means as you
say, if it follows, then you can prove it.
The term "completeness," as it applies to a logic, I believe, is only
as you define it. As it applies to a contentful theory expressed in a
logic, I believe it usually means what I an Baldwin mean.
Second order arithmetic is sematincally complete while it is proof
theoretically incomplete, since second order logic itself is
proof-theory incomplete.
> there will always be models, describe in theories G' that are
extensions of G, as expressed in different applications, that ARE
inconsistent with each other. As in John's example, "an employee must
be at least 21 years of age," may be a rule expressed in one
applicaton, while in another employees may be 16, or have no specified
age limits.
OK, so if you've got a theory G that doesn't entail anything specific
about age limits, then you could extend G to theories G1 and G2 that
specify different age limits. Hence, a model M1 of G1 and a model M2 of
G2 will both be models of G but will be "inconsistent" in the sense
above. Fine, but it seems to me this is all more easily expressed proof
theoretically -- it's the simple logical fact that every consistent
incomplete theory has consistent extensions that are mutually
inconsistent.
you are right, that might be an
easier way to say it, especially if you expand out all my lazy
ellipses. Or else completely (no pun intended) on the model theoretic
side. Mixing the two together is generally a more complex thought to
follow.
The point remains, which was the point of the mail: ontologies do not
guarantee complete "interoperability", but that term probably needs and
does not have a definition. And if ontologies only guarantee something
partial, what is it that they DO guarantee? And why, in practice, do
even primitive but logical shared messaging specifications like the
early tagged syntax S.W.I.F.T provide so much value, and not seem to
lead us into trouble. (While some shared but literally insane
messaging specification like the health care EDI messages create huge
error and correspondingly huge employment opportunities
-chris
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