[seek-kr-sms] OBOE clarifications and questions

Bertram Ludaescher ludaesch at ucdavis.edu
Fri Jun 16 09:27:20 PDT 2006


Hi Sergey: 

I think guarded logics might indeed be interesting and some of the
"alphas" that Shawn and I have used for semantic typing might be of
the right form to fall into those fragments. We might want to look
more into that (see also next email ;-)

BTW, you will have noticed that Graedel's talk and paper I referred to
in the previous mail also includes Guarded Logics.

BTW2, I see that mathematicians are really progressing w.r.t. their
cookie receipts! While I was a PhD student in Freiburg (Breisgau),
I had the pleasure to work some time with Max Kubierschky and his
advisor Prof. Flum (this is a paper that come out of Max' MS thesis: 
http://users.sdsc.edu/~ludaesch/Paper/icdt97.html)

On page 35 of his his thesis
http://logik.mathematik.uni-freiburg.de/preprints/Diplom/kubiers-dipl.ps
he has two recipies for some tasty chocolate cookies (I guess to "beef
up" or rather "sweeten" the somewhat dry mathematical formalism.)

I noticed that the 2nd reference you sent has on page 2 (!!) a recipe
for "waterproof cookies" !! Now that is progress! Given that it's
already on page 2, the work must be very dry... (or is it so
mouthwatering that one needs waterproof cookies..)

curiouser and couriouser ...

:)

Bertram

>>> On Thu, 15 Jun 2006 15:23:56 -0400
>>> "Serguei Krivov" <Serguei.Krivov at uvm.edu> wrote: 
SK> 
SK> Hi Bertram,
SK> Long time ago you and Raja were talking about guarded logics as a decidable
SK> option. As I understand now, here all boolean operations are avalible, the
SK> quantification is restricted; But  if handling tuples of length more then 2
SK> is our main concern then perhaps guarded logics is a possible solution???
SK> 
SK>  I remember, that time I looked at: 
SK> e.g. http://citeseer.ist.psu.edu/gr99decision.html
SK> and then studied:
SK> http://www-mgi.informatik.rwth-aachen.de/Publications/pub/hirsch/hirsch.pdf
SK> 
SK> So, what is your current opinion about guarded logics?
SK> 
SK> sergey
SK> 
SK> 
SK> 
SK>  
>> -----Original Message-----
>> From: seek-kr-sms-bounces at ecoinformatics.org [mailto:seek-kr-sms-
>> bounces at ecoinformatics.org] On Behalf Of Bertram Ludaescher
>> Sent: Thursday, June 15, 2006 2:41 PM
>> To: Shawn Bowers
>> Cc: seek-kr-sms at ecoinformatics.org
>> Subject: Re: [seek-kr-sms] OBOE clarifications and questions
>> 
>> 
>> An addition to Shawn's answer to Matt's question for Josh, which Josh
>> had passed on to Shawn (now let's do an annotation/data lineage graph
>> for THAT! ;-)
>> 
>> Ontologies expressed in description logic have certain limitations in
>> expressiveness. This has to do w/ the fact that DLs are (almost
>> always) decidable first-order fragments of a special kind, i.e.,
>> "2-variable first-order logic". In particular, this means that any
>> individual statement (axiom) cannot--in general--refer to more than
>> two things at one time. Think of the two variables as pointers
>> (pebbles for logic game-theorists). You then make statements about two
>> domain elements. So in general you cannot make statements that require
>> inter-relating 3 or more individuals at the same time (or else you
>> might risk getting into undecidability land..)
>> 
>> On the other hand, there are other logic fragments, most notably
>> conjunctive queries CQ (aka Select-Project-Join queries) which are
>> able to refer to many individuals at the same time. But there you have
>> only existential quantification and no negation.
>> 
>> Mixing CQ and DL in general leads to undecidability.
>> 
>> Shawn: we might want to look up the decision procedure for 2-FO (and
>> DLs in particular).
>> 
>> Maybe there is some interesting research to be done in combining
>> CQ-like fragements with DL for specialized "alpha languages" that are
>> still decidable.
>> 
>> For now, my lips are sealed on any further comments, since this list
>> is googleable ;-)
>> 
>> Bertram
>> 
>> 
>> 
>> >>> 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?
>> For
>> >>> example, a 'site' table, and a 'tree measurement' table that has a
>> >>> foreign key into the site table.  Can we create annotations that refer
>> >>> to attributes in both tables?
>> >>>
>> >>
>> >> I'm not 100% sure what you mean here.  I hope that we can do this.
>> Shawn
>> >> might have a better sense for this question.
SB> 
SB> Matt, we have typically been defining a semantic annotation as a
>> mapping
SB> from relation (database) instances to ontology instances. These
>> 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) &
>> measuredIn(y,x)
SB> 
SB> asserts that if x is a value in the Site table, and x,y are values 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
>> '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 side,
>> and
SB> not for specifying the annotation logic itself.
>> 
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