Sorry for slow reply -- was forced to focus on my day job for a while. (01)
I have reproduced below the relevant details a small OWL ontology in manchester
syntax that illustrates how this works (full version in RDF/XML is attached).
In fact when I looked at your example I realised that transitive over doesn't
work the way I thought -- the "transitivity" seems to be "over" the inverse of
the property named in the transitive over assertion. This seems strange to me
(are you sure it is correct?), but it is immaterial as far as OWL is concerned
-- it can do either. (02)
In this case I introduced a new property "hasConstituent" as the inverse of
"consistsOf", but again this isn't necessary (the inverse of a property can be
used without introducing a name for it). (03)
I then say that worksFor o hasConstituent SubPropertyOf worksFor; i.e., forall
x,y,z . [x worksFor y and y hasConstituent z implies x worksFor z]. (04)
Your example wasn't very clear about whether, e.g., R&D is meant to be a class
(unary predicate) or individual (constant), but again it doesn't really matter
-- I could easily reformulate the example to use classes rather than
individuals (I used individuals in this example). (05)
I created the ontology using Protege 4.1 with the HermiT 1.2.4 reasoner. I can
use Protege to submit queries such as finding all the instances of the class
"worksFor value Semantic_Web", "worksFor value R&D" or "worksFor value X". In
all cases Mikhail_Khlopotov is in the answer (in fact {Mikhail_Khlopotov} the
complete answer). If remove the SubPropertyOf part of the definition of
worksFor, then the answers to all these queries are empty. (06)
I hope this makes everything clear. (07)
Regards,
Ian (08)
ObjectProperty: consistsOf
InverseOf:
hasConstituent (09)
ObjectProperty: hasConstituent
InverseOf:
consistsOf (010)
ObjectProperty: worksFor
SubPropertyOf:
SubPropertyChain:
worksFor o hasConstituent (011)
Class: Company (012)
Individual: X
Types:
Company
Facts:
consistsOf R&D (013)
Individual: R&D
Facts:
consistsOf Semantic_Web (014)
Individual: Semantic_Web
Facts:
consistsOf Semantic_Web_Inference (015)
Individual: Semantic_Web_Inference (016)
Individual: Mikhail_Khlopotov
Facts:
worksFor Semantic_Web_Inference (017)
eg2.owl
Description: Binary data
On 13 Aug 2010, at 23:11, Adrian Walker wrote: (01)
> Hi Ian --
>
> You wrote that "transitive over" can be expressed in OWL2 as follows:
>
> <owl:ObjectProperty rdf:about="&Ontology1280842771883;P1">
> <owl:propertyChainAxiom rdf:parseType="Collection">
> <rdf:Description rdf:about="&Ontology1280842771883;P1"/>
> <rdf:Description rdf:about="&Ontology1280842771883;P2"/>
> </owl:propertyChainAxiom>
> </owl:ObjectProperty>
>
> Would you have time please to add sample data and a query as in [1], and to
>show what is the answer to the query, and which engine was used?
>
> Thanks, -- Adrian
>
>
> [1] www.reengineeringllc.com/demo_agents/TransitiveOver1.agent
>
> Internet Business Logic
> A Wiki and SOA Endpoint for Executable Open Vocabulary English Q/A over SQL
>and RDF
> Online at www.reengineeringllc.com
> Shared use is free, and there are no advertisements
>
> Adrian Walker
> Reengineering
>
>
> On Tue, Aug 3, 2010 at 10:00 AM, Ian Horrocks <ian.horrocks@xxxxxxxxxxxxxxx>
>wrote:
> I believe that the use of property chains in property inclusion axioms, which
>is a new feature in OWL 2, will allow you to express what you want. In essence
>this allows you to assert that a sequence of properties (a chain) implies
>another "short cut" property. If I understand transitive across correctly,
>then asserting that P1 followed by P2 implies P1 is equivalent to saying that
>P1 is transitive across P2. In RDF/XML syntax it looks like this:
>
> <owl:ObjectProperty rdf:about="&Ontology1280842771883;P1">
> <owl:propertyChainAxiom rdf:parseType="Collection">
> <rdf:Description rdf:about="&Ontology1280842771883;P1"/>
> <rdf:Description rdf:about="&Ontology1280842771883;P2"/>
> </owl:propertyChainAxiom>
> </owl:ObjectProperty>
>
> In OWL 2 the chain can include more than 2 properties, and the implied
>property doesn't have to be one of those mentioned in the chain. There are,
>however, some restrictions on cyclical inclusions (needed for decidability).
>
> I'm not sure what you mean by selecting an inference method. OWL doesn't
>specify any particular inference method -- just a semantics. I believe that
>all of HermiT, FaCT++ and Pellet are fully OWL 2 compliant, so they are able
>draw whatever conclusions are implied by the semantics, including the
>semantics of property chain inclusions.
>
> Ian
>
>
>
>
>
>
> On 2 Aug 2010, at 20:01, Adrian Walker wrote:
>
> > Ian --
> >
> > Dave wrote:
> >
> >
> > Unless I’m missing something I think the “transitive over” problem is
>handled in OWL2 with property chains.
> >
> >
> >
> > Is that correct please?
> >
> >
> >
> > If so, could you post the OWL2 code that does this?
> >
> >
> >
> > Does one then still have to know which inference method to select to get it
>to run correctly?
> >
> >
> >
> > Thanks, -- Adrian
> >
> >
> >
> > Internet Business Logic
> > A Wiki and SOA Endpoint for Executable Open Vocabulary English Q/A over SQL
>and RDF
> > Online at www.reengineeringllc.com
> > Shared use is free, and there are no advertisements
> >
> > Adrian Walker
> > Reengineering
> >
> >
> >
> >
> >
> >
> > On Mon, Aug 2, 2010 at 2:39 PM, Ian Horrocks <ian.horrocks@xxxxxxxxxxxxxxx>
>wrote:
> > I don't really know where to start in responding to this, and I only have
>limited time. Here are a few points. I apologise in advance for the fact that
>I am going to have to bunk out of the discussion at this point -- entertaining
>though it is, it doesn't pay the rent!
> >
> >
> > You describe my discussion of robustness as "hopelessly misleading", an
>argument you support by introducing a discussion of the difficulty of
>rendering "ordinary language" into logic. I don't dispute this difficulty, but
>it is completely orthogonal to the discussion we are having (or at least that
>I thought we were having), which is about the computational properties of
>different logics. What I say about robustness is nothing more than simple
>statement of what follows directly from complexity theory.
> >
> > In response to my argument about the incorrect use of reasoners you
>introduce the notion of NAF. This is irrelevant and potentially confusing --
>the failure in NAF refers to "not provably true" and not to the failure of a
>given (incomplete) algorithm.
> >
> > You seem to say that it is best to allow users to write whatever they like
>and then leave it to the reasoner to figure out how best to deal with it.
>Unfortunately, this approach isn't really practicable as users often want or
>need to know what kind of behaviour they can expect from a reasoning system,
>without necessarily knowing the exact problems they are going to be solving.
>Language subsets are convenient ways to define sufficiency conditions for
>(more) robust behaviour (or at least the possibility of more robust behaviour).
> >
> > Many of your arguments, including the above one, seem to presuppose a
>situation in which the reasoning system is used only by expert users -- in
>fact you say that other kinds of users, e.g., those who don't fully understand
>NAF, should avoid using logic or logic based tools. Perhaps, but you might
>equally well declare that only expert programers should be allowed to produce
>software. IMHO it is more realistic (and more useful) to try to develop tools
>and methodologies that help people to do a better (if not perfect) job.
> >
> > Regards,
> > Ian
> >
> >
> >
> >
> >
> > On 2 Aug 2010, at 17:07, John F. Sowa wrote:
> >
> > > Pat, Ian, and Adrian,
> > >
> > > I'm back from my travels, and I'd like to address a few issues
> > > about Cyc, about the many ways of using logic, about "robustness",
> > > and about how any or all of these issues affect practical problems
> > > that people are desperately trying to solve.
> > >
> > > By the way, I'll make some strong positive statements about Cyc
> > > in the following remarks, but I also have strong criticisms
> > > about many aspects of Cyc. But on the particular issues in this
> > > thread, I have a great deal of sympathy with the Cyc approach.
> > >
> > > PH> The real difference here is one of academic style: the CycL
> > >> developers are ruthlessly pragmatic and do not care a whit for
> > >> theoretical analyses of completeness or for proving correctness.
> > >
> > > One has to distinguish the many different "CycL developers". As the
> > > principal stockholder, Lenat has the final say on what directions
> > > are supported. But the complete Cyc system has over three dozen
> > > different inference engines, which are based on a wide range of
> > > different principles.
> > >
> > > Over the past 26 years, Lenat has hired (and fired) some of the
> > > best and brightest logicians, linguists, computer scientists, and
> > > experts in various fields, disciplines, and paradigms. Many of
> > > them have been very sensitive to the theoretical issues, and they
> > > have designed inference engines that are as technically respectable
> > > as any that have come from any academic department.
> > >
> > > Some of the Cyc inference engines process subsets of logic that
> > > are eminently decidable, others use an open-ended variety of
> > > heuristics, and others use very "quick and dirty" methods of
> > > getting results for the "easy" cases.
> > >
> > > IH> OWL's expressive power could, of course, be easily (indeed
> > >> arbitrarily) extended if one were prepared to compromise on
> > >> some or all of these design constraints.
> > >
> > > I suspect that the word 'compromise' is being used as a criticism
> > > rather than a desirable trait. Among the Cyc inference engines,
> > > some are highly disciplined tools that don't make any compromises
> > > with precision or decidability. But the total Cyc system has to
> > > accept anything and everything that anybody might throw at it.
> > >
> > > In that sense, Cyc makes compromises in a positive way: it analyzes
> > > the problem at hand in order to choose which of the many inferences
> > > engines to use. In cases of doubt, it can run more than one in
> > > parallel to see which one finishes first.
> > >
> > > PH> Ian is using "complete" here to mean "complete and decidable",
> > >> which can be characterized as: if a sentence is a theorem, then
> > >> the prover will tell you that - completeness - AND if it isn't
> > >> a theorem, the prover will also tell you that it is not.
> > >
> > > Yes, but I'll also add that a huge number of very practical problems
> > > are handled by model checking rather than theorem proving.
> > >
> > > The SQL WHERE-clause, for example, uses the full power of FOL for
> > > queries, constraints, and triggers. But it doesn't attempt to prove
> > > those statements. Instead, it evaluates their truth value in terms
> > > of a model -- namely, the current state of a relational DB. That
> > > evaluation is done in polynomial time in the worst case, and in
> > > many of the most common cases, in linear or logarithmic time.
> > >
> > > That is the advantage of having a single very expressive language
> > > such as CycL (or Common Logic) and a method for determining which
> > > of the many inference engines (or other tools) to use for any
> > > particular problem.
> > >
> > > IH> In fact such reasoners are typically used in a way that is
> > >>> actually incorrect, in that failure to find an entailment is
> > >>> treated as a non-entailment, whereas it should be treated as
> > >>> "don't know".
> > >
> > > PH> I dont think it is fair to say that they are *typically* used
> > >> in this incorrect way. (?)
> > >
> > > I agree with Pat. The difference between classical FOL and
> > > negation as failure is very well understood by Lenat and the
> > > people he hired.
> > >
> > > The people who don't understand that difference are congenitally
> > > incapable of using *any* logic-based tool in a serious way --
> > > that includes CycL, CL, OWL, and even SQL.
> > >
> > > (Please don't say that non-AI professionals can use OWL, because
> > > I've seen what they've done and it proves my point. For the subset
> > > of OWL they actually use, they'd be better off using simpler tools.
> > > And yes, Adrian, your Executable English would be a good option.)
> > >
> > > IH> I completely agree that being decidable is no guarantee that
> > >> reasoning tools will always work well in practice. We can imagine
> > >> a graph with complexity classes on the x-axis and robustness on
> > >> the y-axis.
> > >
> > > I think we all agree on that point.
> > >
> > > IH> Increasing complexity inevitably means decreasing robustness.
> > >> Robustness is a very important quality of reasoners from a user
> > >> POV -- what it means is that small changes in the input (e.g.,
> > >> the ontology) produce only small changes in the performance of
> > >> the reasoner. We can think of undecidability as simply being
> > >> a very high complexity class, i.e., one where we can expect
> > >> relatively poor robustness.
> > >
> > > Every sentence in that paragraph requires so many qualifications
> > > and caveats that it is hopelessly misleading. First of all, every
> > > version of formal logic from Aristotle's syllogisms to the present
> > > is notoriously brittle, and the primary source of brittleness is
> > > *not* the complexity class.
> > >
> > > The major source of brittleness is the definitions of terms.
> > > Everybody from A to Z (Aristotle to Zadeh) has observed that words
> > > in ordinary language don't have a one-to-one mapping to definitions
> > > in any formal logic.
> > >
> > > URIs that link to formal definitions are irrelevant when the people
> > > who use the terms don't know or understand the definitions. I'd give
> > > Cyc much higher marks in addressing the issue of trying to determine
> > > (i.e., guess) the intended word senses than systems (automated or
> > > manual) that map words to arbitrary URIs.
> > >
> > > I would also question the term 'small changes', the definition
> > > of robustness in terms of relating "small changes", and the
> > > assumption that OWL (or any formal system from Aristotle to
> > > the present) contributes much, if anything to the solution.
> > >
> > > And I repeat the point that decidability depends on what you do
> > > with the logic rather than the expressive power of the logic.
> > > For example, the SQL method of processing an FOL statement is
> > > more robust than most theorem provers -- primarily because the
> > > SQL evaluation takes fewer steps than most proofs.
> > >
> > > IH> There are other users who have the opposite problem --
> > >> they want/need a more expressive ontology language...
> > >
> > > Nobody but a professional knowledge engineer knows what an
> > > ontology language is, let alone what properties it should have.
> > > Those people who have been exposed to talks about such things
> > > are hopelessly confused.
> > >
> > > IH> Bottom line: there is no "right choice" of ontology language.
> > >
> > > I certainly agree with that statement. I'd add that only highly
> > > trained experts (knowledge engineers, logicians, or computer
> > > scientists) are capable of making such a choice.
> > >
> > > I'll also claim that the Cyc software is far more capable of
> > > choosing an appropriate subset of logic and an inference engine
> > > to process it than the majority of people who have been exposed
> > > to lectures about OWL or any other formal logic.
> > >
> > > John
> > >
> > > _________________________________________________________________
> > > Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
> > > Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
> > > Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> > > Shared Files: http://ontolog.cim3.net/file/
> > > Community Wiki: http://ontolog.cim3.net/wiki/
> > > To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
> > > To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
> > >
> >
> >
> > _________________________________________________________________
> > Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
> > Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
> > Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> > Shared Files: http://ontolog.cim3.net/file/
> > Community Wiki: http://ontolog.cim3.net/wiki/
> > To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
> > To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
> >
> >
> >
> > _________________________________________________________________
> > Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
> > Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
> > Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> > Shared Files: http://ontolog.cim3.net/file/
> > Community Wiki: http://ontolog.cim3.net/wiki/
> > To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
> > To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
>
>
> _________________________________________________________________
> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> Shared Files: http://ontolog.cim3.net/file/
> Community Wiki: http://ontolog.cim3.net/wiki/
> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
> To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
>
> (02)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (01)
|