Ed,
Thanks for all these nice examples of context dimensions (financial domain), frames of reference (the definition of a planet), dynamism (the health care domain), and perspectives (the portable hand drill). Actually, you can find elements of all of them in all your examples.
One of the things that NCOIC did a while back is collect different problem space decompositions used in different government and industry domains. We stopped after we collected about 14 major (i.e., commonly used) decompositions. We could not come up with any consistent basis for relating these to each other or to any other overarching categorization principle. And of course, these categorizations were mostly orthogonal to each other (e.g., regional versus lifecycle versus mission/goal-oriented), but there was also considerable overlap (e.g., functional and mission/goal-oriented, such as when the function and the mission/goal more or less aligned with each other). And earlier work in domain analysis that I was involved in also showed both the overlap and the orthogonality of different domains and the influence that choices about domain scope and related domain “boundaries”, however fuzzy they might be, had on the degree of overlap and orthogonality (or should I say degree of “coupling” or “relatedness” among domains?). The thing that struck me was the inherent arbitrariness and extensive social/institutional grounding for domain definitions and boundaries (like the planet issue), as well as the role of perspectives on how domains are viewed by different role players (like your drill example). Another important aspect of these observations was the issue of identity, and how context and perspective-dependent identity is. I suspect that the same parts had different identities in the drill example you gave, especially if they had identifiers in the context of the supplier of those parts as opposed to the context of the assembler/manufacturer of the drill. In the context of the design engineer, they might not even have had part numbers but part names and assembly names. And none of this really matters to the drill user, who might be interested in the chuck size, the RPM/horsepower/power requirement attributes of the drill, and maybe the model number (to order repair parts/assemblies) and the manufacturer/serial number/sale date (if there is a recall or warranty issue). In some contexts, the purchaser of the drill may assign an inventory/property control number to that drill. And if it’s a very expensive, specialized drill, it might have an asset ID in the purchaser’s accounting system. Which points up the arbitrariness of the division between capital assets and expensed items in modern accounting systems. I can remember when just about every computer was considered a capital asset. Now only the most expensive high-end servers meet the (changing) cost criteria.
I’m starting to ramble, so let me terminate this email by underscoring that the multiplicity of categorization systems are inherent in context, perspective and scope variability in reality (including alternate realities). Categorization is itself a potential scope dimension, as in how many different categorization schemas does your system/ontology support/account for (in some absolute count sense), or how many of some set of categories does it support (i.e., some percentage of a specified set), or how much of a specific category or domain does the system/ontology address (e.g., residential vice industrial plumbing, or only US building code plumbing).
One thing we encourage people to do is look at “adjacent domains” and the different perspectives and identifiers that those domains might have with respect to your own “domain of focus”. If forum members are interested, I can forward a copy of such an informal adjacent domain analysis for “friendly force tracking” interoperability with adjacent domains such as command and control, logistics, or personnel management.
Hans
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Ed Barkmeyer
Sent: Thursday, March 08, 2012 4:39 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Constructs, primitives, terms
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
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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
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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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