[seek-kr-sms] OBOE clarifications and questions
Bertram Ludaescher
ludaesch at ucdavis.edu
Fri Jun 16 11:18:50 PDT 2006
Hi Kai:
Thanks for the clarification! Comments below
cheers
Bertram
>>> On Fri, 16 Jun 2006 10:55:32 -0700
>>> "Kai Lin" <klin at sdsc.edu> wrote:
KL>
KL> Bertram,
KL>
KL> I think the actual question is not about the mathematical truths. The
KL> actual question is how to use DL (or OWL DL) to present N-ary relations
KL> and solve our application problems.
Good point. Agreed. It is certainly true for GEON and SEEK!
(neither is in the business of mathematical foundations)
What I meant to say is that we cannot--in general--reason with n-ary
relations (meaning, there is no decision procedure for satisfiability,
once we go beyond certain language classes). That's were the
mathematical truth comes in.
But you're right: I shouldn't have been ranting ;-)
KL> People usually think that DL only
KL> allows binary relations,
that's the "normal case" indeed
KL> but there is a nice way to present SOME N-ary
KL> relations in DL with binary relations. Note that I use the term
KL> "present" instead of "define";
I see.
KL> also not all the N-ary relations can be
KL> presented in DL, but some of them can be presented in DL depending on
KL> the problems. Once a N-ary relation is presented in DL, you get the
KL> ability of DL for free.
ok, the question remains: what can one do w/ these "presentations" ..
KL>
KL> Here is an example which may be helpful for understanding:
KL>
KL> We measure chemical element A on material B and get a value V with a
KL> unit U. To specify it in FOL, we may use a relation Measure(A, B, V, U).
or we can use a triple even (as in F-logic or EAV or RDF), right?
In terms of *representation*, we just need triples. Actually, I wonder
whether one can get away even with a single binary relation (and
a powerful underlying universe ..)
KL> To present this 4-ary relation in DL, we define a new class Measurement
KL> and 4 properties:
KL>
KL> subject : Measurement -> Material
KL> object : Measurement -> Element
KL> value : Measurement -> int
KL> unit : Measurement -> Unit
KL>
KL> In other words, a measurement is a composition of a element, a material,
KL> a value and a unit. You can add DL constraints on these properties.
OK, to me this looks like the class Measurement is a unary predicate.
There are 4 binary relations (called subject/2, object/2, value/2, and
unit/2, respectively) that associate a Measurement with one things
such as Material/1, Element/1, int/1, and Unit/1.
So there is not really a 4-ary relation here, but 4 binary relations
and a bunch of unary ones.
I think we kind of agree here :)
KL> Obviously not all the FOL constraints can be translated into DL
KL> constraints. For real applications, DL may be enough, may be not.
correct. But the above example stays within the realm of conventional
DL it seems (no real n-ary relations are used).
KL> That W3C document tells us some other patterns we can used to PRESENT
KL> n-ary relations in DL. They are just some useful tricks, not theory at
KL> all.
I think I see your point. I agree that with "tricks" like the above,
one can get representations of n-ary relations via n binary
relations. It seems to make a big difference also what assumptions we
make about the underlying UoD, i.e., whether we have "complex" domain
elements or not.. The Ebbinghaus-Flum logic book has a discussion on
that (need to look up the reference again..)
cheers
Bertram
KL>
KL> -- Kai
KL>
KL>
KL>
KL> -----Original Message-----
KL> From: Bertram Ludaescher [mailto:ludaesch at ucdavis.edu]
KL> Sent: Friday, June 16, 2006 9:02 AM
KL> To: Kai Lin
KL> Cc: Bertram Ludaescher; seek-kr-sms at ecoinformatics.org
KL> Subject: RE: [seek-kr-sms] OBOE clarifications and questions
KL>
KL>
KL> Kai:
KL>
KL> Great to hear from you! I need to check out that reference more
KL> carefully... But I can already say that no matter what the W3C says,
KL> there are mathematical truths that are above the W3C standardization
KL> processes and that by their very nature will outlast W3C, the Web, the
KL> life span of mankind, the biosphere (life on planet Earth), and maybe
KL> the universe/multiverse itself (ok, I'm getting a bit more speculative
KL> towards the end ;-)
KL>
KL> If I want to relate n objects simultaneously, I can use, e.g., an
KL> n-ary relation symbol R(A1,..., An), or I can use a first-order
KL> formula with n free variables.
KL>
KL> However, in general I can no longer decide satisfiability (and related
KL> notions) in such first-order fragments.
KL>
KL> I just came across the following very nice material that might shed
KL> some light on this -- here are the slides:
KL> http://www-mgi.informatik.rwth-aachen.de/~graedel/kalmar.pdf
KL> (e.g. slide #53 shows how one can express the existence of a path of
KL> length 17 in FO2, i.e., in FO w/ only two variables.
KL>
KL> And here is the paper that apparently goes with the slides:
KL> http://citeseer.ist.psu.edu/631148.html
KL>
KL> enjoy!
KL>
KL> Bertram
KL>
KL>
KL>
>>> On Thu, 15 Jun 2006 12:37:57 -0700
>>> "Kai Lin" <klin at sdsc.edu> wrote:
KL>
KL> Bertram,
KL>
KL> I am not sure that I understand the context of the discussion.
KL> Actually
KL> it is possible to specify N-ary relations in OWL or RDF. The OWL
KL> working
KL> group in W3C has a formal document on this issue. You can find it at
KL> the
KL> following URL:
KL>
KL> http://www.w3.org/TR/swbp-n-aryRelations/#vocabulary
KL>
KL> Best,
KL>
KL> -- Kai
KL>
KL>
KL> -----Original Message-----
KL> From: seek-kr-sms-bounces at ecoinformatics.org
KL> [mailto:seek-kr-sms-bounces at ecoinformatics.org] On Behalf Of Bertram
KL> Ludaescher
KL> Sent: Thursday, June 15, 2006 11:41 AM
KL> To: Shawn Bowers
KL> Cc: seek-kr-sms at ecoinformatics.org
KL> Subject: Re: [seek-kr-sms] OBOE clarifications and questions
KL>
KL>
KL> An addition to Shawn's answer to Matt's question for Josh, which
KL> Josh
KL> had passed on to Shawn (now let's do an annotation/data lineage
KL> graph
KL> for THAT! ;-)
KL>
KL> Ontologies expressed in description logic have certain limitations
KL> in
KL> expressiveness. This has to do w/ the fact that DLs are (almost
KL> always) decidable first-order fragments of a special kind, i.e.,
KL> "2-variable first-order logic". In particular, this means that any
KL> individual statement (axiom) cannot--in general--refer to more than
KL> two things at one time. Think of the two variables as pointers
KL> (pebbles for logic game-theorists). You then make statements about
KL> two
KL> domain elements. So in general you cannot make statements that
KL> require
KL> inter-relating 3 or more individuals at the same time (or else you
KL> might risk getting into undecidability land..)
KL>
KL> On the other hand, there are other logic fragments, most notably
KL> conjunctive queries CQ (aka Select-Project-Join queries) which are
KL> able to refer to many individuals at the same time. But there you
KL> have
KL> only existential quantification and no negation.
KL>
KL> Mixing CQ and DL in general leads to undecidability.
KL>
KL> Shawn: we might want to look up the decision procedure for 2-FO (and
KL> DLs in particular).
KL>
KL> Maybe there is some interesting research to be done in combining
KL> CQ-like fragements with DL for specialized "alpha languages" that
KL> are
KL> still decidable.
KL>
KL> For now, my lips are sealed on any further comments, since this list
KL> is googleable ;-)
KL>
KL> Bertram
KL>
KL>
KL>
>>> On Wed, 14 Jun 2006 11:14:38 -0700 (PDT)
>>> Shawn Bowers <sbowers at ucdavis.edu> wrote:
SB>
>>> 3) How to deal with multiple relations with integrity constraints?
KL> For
>>> example, a 'site' table, and a 'tree measurement' table that has a
>>> foreign key into the site table. Can we create annotations that
KL> refer
>>> to attributes in both tables?
>>>
>>>
>>> I'm not 100% sure what you mean here. I hope that we can do this.
KL> Shawn
>>> might have a better sense for this question.
SB>
SB> Matt, we have typically been defining a semantic annotation as a
KL> mapping
SB> from relation (database) instances to ontology instances. These
KL> mappings
SB> have signatures of the form (where a is the annotation)
SB>
SB> a: R1 x R2 x ... x Rn -> O1 x O2 x ... x Om
SB>
SB> such that R1 to Rn are relations (tables) and O1 to Om are ontology
SB> classes and properties. For example, the annotation
SB>
SB> a: Site(x) & Tree(x, y) -> StudyArea(x) & TreeMeasure(y) &
KL> measuredIn(y,x)
SB>
SB> asserts that if x is a value in the Site table, and x,y are values
KL> in the
SB> Tree table, then x is an instance of a study area concept, y is an
SB> instance of a tree measure concept, and there is a property
KL> 'measuredIn'
SB> from y to x.
SB>
SB> OBOE is only concerned with providing a useful vocabulary for the
SB> right-hand side of these rules. Not for specifying the left-hand
KL> side, and
SB> not for specifying the annotation logic itself.
KL>
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