Andrea,
I think we agree in part about axioms and constraints. Unlike data modeling for a known set of applications, in making an ontology you have to sort out two
kinds of axioms/constraints – definitive and pragmatic. A definitive axiom is one that is required for understanding of the concept, and usually, to distinguish it from other related concepts. E.g.
A toxic fluid is a fluid that has at least one component that is harmful to humans who are exposed to it by skin contact, eye contact or
inhalation.
The constraint is a definitive axiom for ‘toxic fluid’, as distinct from other fluids. (This is the kind of thing that many weak taxonomies fail
to express formally, if at all.) This might be formally phrased as: F is a toxic fluid if and only if F has at least one toxic component, or even just :
Each toxic fluid has at least one toxic component, where ‘toxic component’ is a primitive type in the ontology with the above natural language definition. The point is that, however phrased, this axiom cannot be separated from the module that introduces
the term ‘toxic fluid’ without robbing the term of its primary semantic load.
Conversely, a pragmatic axiom/constraint usually conveys some kind of “business rule”. E.g.,
Each pipeline carries exactly one process fluid.
This is a business decision that simplifies issues of safety and maintenance, but it hardly applies to all process lines in the industry. (Ron
Ross would call it an ‘operational rule’.) The reason why people put axioms like this in their data models, is that their processing application software may be written to expect that this is true, and will lose information or produce nonsense results or crash
if the rule is violated. So you want your database integrity check to flag the second process fluid entry for a given pipeline as an error, instead of implementing the Insert and fouling up any number of application runs. But rules like this have no place
in reusable ontologies.
In some one of our presentations on semantic mediation, we carefully distinguish the reference ontology from the business rules. In supply chain
management in particular, the ontology is reusable, but the business rules often change from one business partner to another.
So, in this sense, I agree completely that the pragmatic ‘axioms’ should be separate from the reusable module.
-Ed
From: ontology-summit-bounces@xxxxxxxxxxxxxxxx [mailto:ontology-summit-bounces@xxxxxxxxxxxxxxxx]
On Behalf Of Andrea Westerinen
Sent: Wednesday, January 29, 2014 9:23 PM
To: Ontology Summit 2014 discussion
Subject: Re: [ontology-summit] [Reusable Content] Characterizing or measuring reuse
Ed, Thanks for the clarification. I would agree with you regarding the concept of consistency as defined by axioms.
However, I was also advocating for 1) more modularity (as you point out) and 2) separation (from the entity declarations) and acknowledgement of the axioms. In this way, there is the possibility for the axioms to be reused (or not) or
evolved.
To be clear, I am not saying that simply splitting the axioms from the entity declarations is sufficient to mend a basic difference in semantics and allow reuse where it is not reasonable. But, it may be sufficient to overcome minor contradictions
by defining different but still semantically relevant axioms.
Thanks for continuing the dialog to clarify and tease apart the concepts ...
On Wed, Jan 29, 2014 at 3:34 PM, Barkmeyer, Edward J <edward.barkmeyer@xxxxxxxx> wrote:
Andrea,
When I said “consistent”, I meant it in the formal logic sense:. If I propose all the axioms in
the two theories, I cannot infer a contradiction.
Now, I may import an ontology that describes a single general concept and has many subclasses and
properties that I can use, and other aspects I don’t care about. It is very unlikely that incorporating that ontology will produce inconsistencies, as long as I agree with the statements about the elements I intend to reuse.
But consider, for example, the case in which I import an ontology for time. It will have a very
small number of undefined terms with characterizing axioms, and quite possibly a rather large set of well-defined terms for derived concepts, some of which I use. Again, I can see pretty clearly whether the parts I use are consistent. But suppose the time
ontology says that a time interval can be started by an event, and it provides a number of axioms that characterize its “event” notion. In my ontology, I want to use that idea, but I have an elaborate model of events and activities. Now I need to be sure
that the imported axioms for ‘events’ (or whatever symbol I equate) don’t contradict my axioms, directly or indirectly. If there is a contradiction, we don’t mean the same thing by “event”. I can still use the imported ontology if I have some class that
satisfies the imported event axioms (a “mapping”), but the import is only useful if I agree that that, or some subclass of it, is the class of things I want to use as the start of time intervals. Further, if my intended use is a subclass of the imported
“event” concept, I need to know that admitting instances of the imported class that I don’t intend to use as the starts of time intervals won’t contradict something I say about activities and time. In particular, consider the case where the imported ontology
says that every event starts the time interval in which that event “has happened”, and implicitly all subintervals thereof that start at the same instant. If his ‘event’ includes things that my model says have a non-zero duration, and I consider those ‘events’
not to “have happened” until that duration has elapsed, there are some small intervals in which the imported model says the event ‘has happened’, but my model says the event ‘has not happened’ but ‘is happening’, which is a different state. Then there exist
events e and time intervals t in which my theory says (not (hasHappenedin e t)) and the imported ontology says (hasHappenedin e t), which is a contradiction.
There is clearly an underlying inconsistency in intent, but it is only a logical inconsistency if
I care about the specific behaviors of things that are accidentally included in his somewhat larger category. This is a version of Pat Hayes’ “Horatio principle” – “there are more things in (my) heaven and earth, Horatio, than are dreamt of in your philosophy”
(Hamlet, Act I).
As Gary (?) pointed out, this is why you would really want these ontologies to be as modular as possible.
If the imported ontology for “events and time” includes, but is separate from, the imported ontology for “time”, I can import the latter without creating the problems engendered by importing the former, even if I really wanted the kind of thing the former
covers, and have to develop that part separately. And it would be a different kind of “reuse” if in that ‘separate development’ I take his “events and time” ontology and MODIFY it to be consistent with my events and activities module. I think this latter
is a pretty common form of ‘reuse’. (I am reminded of Tom Lehrer: “Don’t let others’ work evade your eyes, ... but plagiarize, plagiarize, plagiarize (only be sure always to call it, please, ‘research’).”* J)
-Ed
* from “Lobachevsky”, Tom Lehrer, 1960.
Gary and Ed, There are two bullets in the reuse discussion where I (somewhat) disagree ...
- the content is consistent with the micro-theory adopted by the re-user
- the re-user is able to determine that the content is consistent with his/her theory
Yes, I guess that we might look for structural consistency which was perhaps handled in the conversion
process mentioned previously, the logical consistency (check with a reasoner?) and consistency with the
user's conceptualization.
I don't think that the content must be consistent, but the content must be mappable or translatable.
This takes us back to Hans' point about understanding the assumptions and context of the original content ... Just as more discussion showed that the events in Pascal's talk and
in FIBO were semantically close (if not equivalent), it is important to somehow enable a similar line of reasoning. We need to understand how and why some model was created/defined as it was, and then other alternatives/possibilities that the model enables.
The problem here (as Cory noted) is time and money to create the information or have the dialog. Is this something that could be crowd-sourced?
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