Matthew, "ontology x is accurate" iff all axioms in x are true.
I think closer to what you may mean is: “Ontology X is accurate” iff all inferences from the axioms in X are true, within the scope of the application of the ontology.
No, that's not what I mean. First, I don't really understand what "true within the scope of the ontology" is supposed to express. Whether an axioms is true or false does not depend on the scope of an ontology. The axiom (part_of audi volkswagen) is out of scope for an ontology of human anatomy, but its irrelevance does not make the axiom less true.
Second, I don't see the need to explicitly talk about all inferences from the axioms as long as we are concerned with ontology languages that are based on truth-preserving deductive inference systems like Common Logic or OWL. If all the axioms in X are true it follows that all inferences from the axioms in X are true.
Following Vrandecic "Ontology Evaluation" in "Handbook on Ontologies, Second Edition" (with some modification), I think we need to distinguish (among other things) four questions: - Accuracy: Is the content of the ontology true? - Completeness: Is the domain of interest appropriately covered (this includes terminology as well as axioms)? - Conciseness: Does the ontology irrelevant classes, relations, or axioms? - Redundancy: Are some axioms redundant because they are already entailed by other axioms?
(Vrandecic considers both redundancy and conciseness, but lumps them in the same category.) Of these four questions two (completeness and conciseness) can be answered only with respect to a given set of requirements, because the requirements will determine the scope of the ontology and the necessary depth of the axiomatization. Redundancy is independent of any requirements, but it depends on the choice of the logic (or, more specifically, its entailment relationship). Accuracy depends on neither requirements nor entailment relationship.
The point I try to make in my last email is that even an ontology that contains false axioms might be able to meet all requirements of a given application. This might be because the application never uses the axiom. (E.g., if the application uses only the taxonomy of the ontology, it does not matter if some parthood axioms are wrong.) A more interesting case is the one I mentioned in my last email, where false information in the ontology enable the proper functioning of a larger application. This can be the case because the false axioms are "close enough" to make no difference or because the larger application accommodates the errors in some form.
Best Fabian
On Dec 28, 2012, at 10:26 AM, Matthew West wrote: Dear Fabian, I don’t think this: Obviously, this allows for the possibility that an inaccurate ontology might meet the requirements of a given application. Follows from this: "ontology x is accurate" iff all axioms in x are true. I think closer to what you may mean is: “Ontology X is accurate” iff all inferences from the axioms in X are true, within the scope of the application of the ontology. Regards Matthew West Information Junction Tel: +44 1489 880185 Mobile: +44 750 3385279 Skype: dr.matthew.west This email originates from Information Junction Ltd. Registered in England and Wales No. 6632177. Registered office: 2 Brookside, Meadow Way, Letchworth Garden City, Hertfordshire, SG6 3JE. From: ontology-summit-bounces@xxxxxxxxxxxxxxxx [mailto:ontology-summit-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Fabian Neuhaus
Sent: 27 December 2012 17:39
To: Ontology Summit 2013 discussion
Subject: Re: [ontology-summit] Reasoners and the life cycle Michael, I agree that the appropriate level of detail is dependent on requirements. But I also think that there is a notion of "accuracy" that is not dependent on context or requirements. For this reason I think it is useful to distinguish two notions: accuracy and completeness. I use the terms in the following way: "ontology x is accurate" iff all axioms in x are true. "ontology x is complete (given a set of requirements)" iff (a) x contains all classes, relations that are needed to represent a piece of reality sufficiently to meet the requirements, and (b) x contains sufficient axioms that are needed to answer queries that are relevant for the requirements (given an appropriate theorem prover) Obviously, this allows for the possibility that an inaccurate ontology might meet the requirements of a given application. For example, you might include the axiom (pi = 3.1415), which is inaccurate but might be sufficient for the needs of an application. On Dec 23, 2012, at 4:57 PM, Michael F Uschold wrote:
The examples you give are good, but seem unlikely to turn up in most ontologies people are building because the logics used are not designed to support heavy computation. The fact that different representations that are all important but logically inconsistent seems a great argument that logic is not the best tool for the job of representing all three things in a unified framework. I think the more important point is that "accuracy" is not absolute; there is some notion of context or purpose that is relevant. Something can be accurate enough for one purpose, but woefully inadequate for others. Ideally both representations can seamlessly live together zooming in and out to the appropriate level of detail -- but this may not be possible, as in the cases you note. On appealing to authority: Perhaps you missed my smiley - it was a rhetorical comment. Michael and Alan,
MFU > There is a broader issue here that reasoners are only a part of. That is:
> "Where do you derive confidence from that your ontology is accurate"? Accuracy is important, but it's only one of many features that make
an ontology good. Sometimes, *less* accuracy is better.
For example, relativity and quantum mechanics are known to be
more accurate than Newtonian mechanics. But Newtonian mechanics
is preferable for large objects moving at typical speeds on earth.
As another example, the Navier-Stokes equations for fluid mechanics
are accurate, but too complex for efficient computation. Therefore,
nearly every application uses some approximations. Sometimes, the
*same* application may use *contradictory* approximations for
different aspects: laminar flow, turbulent flow, subsonic flow,
supersonic flow.
MFU > There is a nice tool called Ontology Pitfall Scanner which allows
> you to upload an ontology and it will do a bunch of things like this. I checked the web site, and I noticed that many of the tests it performs
can also be determined by the FCA tools (Formal Concept Analysis). But
FCA can also *generate* the hierarchy automatically in form that is
guaranteed to avoid those pitfalls.
MFU > Still other ways to derive confidence that the ontology is accurate
> is to have it checked by experts in the field. Yes. That is a good example of how one should appeal to "authority".
See my further comments on that point below.
But first, I'd like to cite Alan Rector's points on another thread:
AR
> Ambitions for global "reference terminologies" lead to artefacts built
> by committees some of whose originators - e.g. IHTSDO/SNOMED CT -
> even disclaim responsibility for how they should be used...
>
> Large scale reference ontologies - or models of any kind - can also
> be caught by conflicts of requirements from multiple potential users
> - clinical care, statistical reporting, billing, speed of use, etc.
>
> The results have not always been happy.
These are examples of "too many authorities spoil the broth".
JFS
>> Jim [Hendler] said that he liked the article very much: MFU > Hmm, the subtext here is scarily close to the fallacy of appealing
> to authority. If Jim liked it it must be good. I cited Jim in self defense. He is known to be one of the chief
promoters of the Semantic Web, but I've been known to criticize
many aspects of it.
In any case, citing authority is not, by itself, a fallacy. Every
academic paper cites authorities, and any paper without such citations
is suspect. What is wrong is a *fallacious* appeal to authority:
Linus Pauling was a brilliant physicist.
Linus Pauling said that megadoses of vitamin C are beneficial.
Therefore, megadoses of vitamin C are beneficial.
This reasoning is fallacious for two reasons: (1) being an expert
in physics does not necessarily mean that one is an expert in
medicine; and (2) even among experts in medicine, there is no
consensus that megadoses of vitamin C are beneficial.
Re Semantic Web: Jim Hendler is an acknowledged expert, and he has
been highly supportive of its development. I cited his authority
as evidence that my points are compatible with that development.
John
-- Michael Uschold
Senior Ontology Consultant, Semantic Arts
http://www.semanticarts.com
LinkedIn: http://tr.im/limfu
Skype, Twitter: UscholdM <ATT00001..c>
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