Re: [ontolog-forum] Foundation ontology, CYC, and Mapping

[Ali Hashemi <ali.hashemi+ontolog@xxxxxxxxxxx>]

Hi Pat,

[PC]Thanks for presenting the contrary position.

Two important things. 

(1) it is not _*the*_ contrary position, it is simply _*an*_ alternative. 


(2) you have mis-characterized the alternative presented, nowhere am I talking about hand mappings between the target ontologies directly.

I have no idea where you concluded that i was advocating mappings directly between two particular ontologies.... If you read my response, I was talking about ontologies being plugged into a referent ontologies in the repository. Not direct one-one.


For example, my manufacturing ontology need not plug into another manufacturing one directly; instead, the process modules would map into a family of process ontologies (they need not be logically consistent). Similarly for agents, actions etc. It is using the hub-spoke model. No silly single to single ontology shenanigans here. However, no decreed FO is necessary either. You pick whichever modules are a best fit given that you know a bit about your domain and what is relevant to know. In effect, whatever referent family of ontologies you pick will be your de facto "FO" if you wanna call it that. You need not specify a global FO beforehand. You can try, and it might or might not be helpful. It certainly wouldn't hurt for someone to try.

But to claim that an FO is absolutely essentially to largescale interoperability is ridiculous.

The Euzenat paper is dealing with Description Logic ontologies and the types of mappings available there. Since most of the semantics are external to the system of representation, you are forced to indirectly, implicitly try to derive mappings. Hence the need for a confidence measure (cause you're never really sure what was intended). In our paper, we don't need the confidence measure, as the confidence is generated from the axioms / mapping. So talking about a confidence measure when talking about mappings between ontologies with first order expressivity is largely superfluous. 


I agree the two approaches aren't conflicting, i just wanted to emphasize that an FO is NOT NECESSARY for large scale interoperability. It might be useful, but it is not necessary.

Rest of the responses are inline.

I emphasize that the goals of mapping between domain ontologies and using the FO are not incompatible, I just believe that there are things you can do with an FO that are not possible or not practical by trying to map among multiple ontologies without generating an FO.   You seem to think that specific mappings will be adequate.  But I am especially concerned with information on the internet for which the ontology has not been mapped to yours.   The FO covers that case automatically, I can’t see how specific mappings can.

 

This paragraph makes me think you have completely misunderstood what I was saying. See above.  The FO doesn't cover anything automatically. If it is somehow broad enough to cover all possible intended meanings, then it simply means that a mapping might be generated. You still have to generate the mapping. You are simply mapping into an FO instead of other modules in the repository. It changes nothing.

[[PC]]  The cases I have seen where pluggable modules exist and don’t depend on some ontology of more fundamental concepts to specify the meanings in the modules cover a tiny, **tiny**  fraction of what one would need in an ontology useful for practical purposes.  Perhaps I have missed some important developments.  Can you provide me with examples of applications using ontologies developed from pluggable modules?

PSL and OntoSTIT come to mind. In fact, every core hierarchy in COLORE at the moment  requires no "primitive" from more fundamental concepts for practical purposes. If I want to use PSL, I do not need to go and find an upper ontology to plug it into. It is good to go.

In COLORE, there are 80 ontologies organized into about 11 families of ontologies. There are many many many more families of ontologies, the ones currently included hardly cover the breadth of what's expressible. I would hardly call ontologies for Duration, Temporal, Processes, Geometries, Orderings etc toy ontologies.

If you wanted, you _could_ attach each to an FO, but as they are now, they are all agnostic about many of the issues an FO forces you to take a stand on. However, feel free to see if you can determine a set of primitives that unify them! This is why COLORE exists, so people can test out ideas given a repository of connected ontologies...

[[PC]] How would the hubs be connected to each other?  If the mappings are not 1 to 1, what kinds of relations would have to be defined?  Would you introduce new more basic elements to create the translations among the 7-8 hubs?  Would accurate translations be possible?  (If they are 1 to 1, the ontologies are essentially identical, a case I have never seen).

There are N hubs, because their views are irreconcilable, if they were reconcilable, then they could be merged. This is, I suspect is one of the issues Pat H (and John) have also been going on about. There likely will never be a single view which accommodates every possible perspective.

The hubs are connected via partial mappings. If two people are plugged in using two distinct hubs, then there may or may not be complete fidelity in message passing available. All that is needed for interoperability is to know where and how you agree and disagree. The mappings between the hubs specify agreement and disagreement.

 Here’s a dichotomy:  (1) two candidates for an FO are logically contradictory.  Attempted mappings without stringent effort to isolate and avoid the inconsistency may cause disastrous errors in translation among them.

(2) the two candidates are not logically contradictory.  IN that case they should be able to be merged.  It may take considerable effort, but if the original ontology developers are around to resolve ambiguities as the mapping process takes place, it should be possible.  Without the originators available, in general the ambiguities will leave considerable uncertainty and make mapping highly error-prone.  Except for CYC, the ontologies I have seen in general have many ambiguous types and even more ambiguous semantic relations.

Sure, if you can merge two go for it. I am not sure what the point of this paragraph is. This horse carcass is now a skeleton, let's stop beating it. All you need to know is if they agree, if they don't fully agree, then you need to know where they don't agree as well. Once this is done, you have enough information to accurately pass messages between the two.

 And the best way to avoid ambiguities is to have the domain ontologies specified using a common set of primitives, which have been thoroughly reviewed and tested and documented to be sure that their meanings are clear.

 

If we're talking about ontological meaning, any set of primitives that are general enough to accommodate most views will likely be a single label name. I.e. primitive = Time. No axioms, because they diverge immediately. Fine, if you wanna call this a primitive, so be it. It's utility is minimal from a logical perspective. Anyway, maybe you'll end up with a useful axiom or two. I've expressed this point before and there's nothing new year. I will admit that it is hard to say for sure that this will definitely happen without trying, so go for it. I hope you end up with more than labels!

[[PC]]  Sure, if you have enough metadata - but the point I was making was that creating the metadata to do such mappings is going to be a lot faster if you develop an FO with primitives.  If you have a merge engine that can actually properly relate ontology elements in independent ontologies, it will in effect be using an FO with primitives, except for those minority of cases where there are accurate 1-1 maps for all ontologies in the mix.

This paragraph makes me believe you have not understood what I was saying...  See the initial post and the comments above the inline ones. I don't assume the metadata exists. If it does, then we can traverse the metadata and use information from there to aid us. If the metadata doesn't exist, then you'll have to generate them.  This is independent of whether an FO exists or not.

[[PC]] I will certainly be interested in seeing the concrete results of any mapping tool that appears to perform well enough to sustain some level of accuracy over an inference chain of say 6 to 12 in length.  The paper you referenced by Euzenat surveying ontology mapping indicates the problem that makes me despair. An F value of less than 80% may be interesting and potentially useful for generating search results to present to humans, but is utterly hopeless for logical inferencing.  And what I am aware of seems to be the easy part.  Since all of the meaning in an ontology comes from the logical inferences generated by the semantic relations, the most important matching would be for the semantic relations.  Can you point me to a specific paper that shows promising results for that task?  Is your thesis accessible on-line?

 

Again, confidence measures are superfluous in the context of FOL where the relevant semantics are available. If you have underspecified entities, then you might have to resort to such measures, otherwise you can draw on model theoretic and proof theoretic results to guarantee the mapping. Yes, you can find my thesis in the UofT library ( https://tspace.library.utoronto.ca/handle/1807/17512 ). I should note that the vocabulary used for semantic mappings in the thesis is underdeveloped. It is now grounded in much more accessible mathematics and there have been significant revisions to the procedure for the semantic mapping module and to the algorithm for axiom generation.
 

[[PC]] There may well be parts of the FO that can be segregated out as modules (I have separable modules in the COSMO, such as one for mapping the ontology to databases, with database-specific types and relations), but there will have to be an indispensable framework that integrates the modules, and my experience with COSMO suggests that that would be well over half the ontology.  I also anticipate that users will want a tool that takes the FO and some domain ontology specified using the FO, and extracts from the FO only those elements required to create the domain ontology.  This would be useful to minimize the resulting ontology for computational efficiency, and would  not require that the FO be modularized (though that wouldn’t hurt).  In general it will be unpredictable what modules are needed for the next ontology you encounter on the internet.  See the next comment.

 

This is an important point. There are no widely accepted definitions / guidelines as to what modular means in the context of ontologies. SUMO is occasionally claimed to be modular, we've had difficulty identifying it as such. It would be helpful to agree on what we mean when we say, X is "modular." For an example of a well developed modular ontology written in CLIF, check out PSL ( http://www.mel.nist.gov/psl/ ).

[[PC]] Fine for any two ontologies that are directly hand-mapped.  What do you do for information posted in the internet, assuming that you have the ontology the posting group  uses?   How accurate would an automatic mapping be under those circumstances?  The merging process for different ontologies can be automatic and accurate if the elements of domain ontologies are logically specified only from elements from a common FO. 

Nope, this result extends to ontologies that are also not "hand-mapped". If I have an ontology specified with at least first order expressive, I can trawl the repository and find the best modules which map that description. If I want, I can restrict my search space to a particular type of ontology families - i.e.  the information posted is about energy consumption in houses, i will search the family of mathematical ontologies and really any family of ontology that is related to that energy or human behaviour domains.

That's really all there is to it. If my automatic engine finds some mapping, then great. If I want to use stronger results such as representation and characterization theorems, right now no computer is good enough to produce these automatically, except for the most trivial cases. So for those stronger results, human intervention is required. However, the automated mappings will have identified a weaker form of these results for me already and I can start exchanging certain types of messages with 100% confidence.

All of this is independent of the existence of an FO. It *might* be the case that the internet ontology best fits into an FO. Regardless, the mapping would generate a type of interpretation from the target into the referent (whether FO or other). Computing today is incapable of generating representation theorems or characterization theorems, so i'd still need to do that with human intervention. Whether the mapping is into an FO or other referent ontology does not change this fact.
  

But I cannot visualize how any automatic mapping can achieve any level of accuracy without the use of a common standard of meaning that can express all the elements in the ontologies to be mapped.  I would be fascinated if you could show an example of a mapping between independently developed practical-sized ontologies (non-toy ontologies, used in some application) that can give a mapping accuracy of at least 99% for both classes and relations.  Or at least outline a procedure that you think can do that.

Sure, check out the FOIS 2010 paper  (www.reseed.ca/ali 2nd paper), a mapping is derived between a very common mereotopology (used to specify Part-Whole and Connection relations), and Stone Lattices, a result from mathematics.

Another example from that same paper: modules of PSL map into graph theory, linear orderings etc. All of these are non toy examples. Pretty simple. No FO needed. Accuracy in both is 100%... Though i'm only guessing at what you mean regarding accuracy. For RCC -- Stone, it is 100%. For PSL, using reducibility as defined there, we know with 100% accuracy, what each of its modular components map into.

Best,
Ali

-- 
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