[seek-kr-sms] OBOE clarifications and questions

[Serguei Krivov]

Hi Bertram,
Long time ago you and Raja were talking about guarded logics as a decidable
option. As I understand now, here all boolean operations are avalible, the
quantification is restricted; But  if handling tuples of length more then 2
is our main concern then perhaps guarded logics is a possible solution???

 I remember, that time I looked at: 
e.g. http://citeseer.ist.psu.edu/gr99decision.html
and then studied:
http://www-mgi.informatik.rwth-aachen.de/Publications/pub/hirsch/hirsch.pdf

So, what is your current opinion about guarded logics?

sergey



 
> -----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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