Leo, (01)
Thanks for all that information. Very helpful. (02)
rgds,
Charles. (03)
On Sat, 09 Aug 2003 15:54:16 -0400, Leo Obrst wrote: (04)
>
> Charles,
>
> In general ER does not have built-in transitivity
> relations, e.g., the
> subclass taxonomic backbone (or, equivalently, a
> transitivity property
> declared on a particular, relation). In a real sense,
> there is a
> difference in the set of axioms between ER and (even)
> simple KR
> (knowledge representation) systems/languages, which
> make KR
> systems/languages more expressive. I say
> "systems/languages", though
> they are all best initially expressed as formal
> languages having their
> own syntax and semantics, and then implemented in a
> system. So really,
> language is first and system second.
>
> Relations among relations is actually very important,
> though you can
> have a KR/ontology language in which only concepts
> exist, and thus
> entities and relations are just the same first-class
> citizens, i.e.,
> concepts.
>
> In the simple case, a relation can have sub-relations,
> i.e., parent-of,
> mammal-parent-of, human-parent-of, etc. Works-at the
> parent of both
> works-at-for-profit-company and
> works-at-nonprofit-company, etc. These
> sub-relations typically narrow the range argument, but
> obviously can
> narrow both the range and the domain: e.g.,
> mammal-parent-of probably
> narrows the domain and range.
>
> Slots are a bit peculiar in (most) frame languages
> insofar as they are
> kind of like "directed" relations, i.e., a relation
> that has built-in
> "roles", where the source of the slot is the somehow
> important or
> primary member or focus of the relation, and the
target
> is the secondary
> member of the relation.
>
> The relation between a parent and a child for example
> is just one
> relation. But sometimes you want to emphasize one side
> of the relation
> vs. the other, i.e., by making two relations parent-of
> and child-of,
> respectively. I.e., inverse relations. This is kind of
> more
> "user-friendly", as Bob MacGregor has noted. In some
> systems, there is
> just one relation, but there are two roles. In OO
> systems, this might be
> expressed as two functions "parents" (as opposed to a
> relation
> "has-children") and "children" (as opposed to a
> relation "has-parents").
>
> In general, I think that the more you get involved
with
> ontologies and
> semantic modeling, the more you like the logical
> notions of axiomatic
> systems as opposed to frame and OO languages. Things
> are much clearer
> and precise.
>
> Leo
>
> Charles Armstrong wrote:
> >
> > Leo,
> >
> > A very interesting post.
> >
> > I have been trying to understand the differerences
> > between OO and Frames. The main one I can see is
that
> > Slots have a degree of independence from the
Concepts
> > they connect. So you can extend the Slots
themselves,
> > which you can't really do with OO relations.
> >
> > Please could you give me an example of where this is
> > useful (I can't think of one, but that is probably
> > because my mind thinks in OO terms).
> >
> > Also are there any other differences in the
> > Entity/Relationship struture between OO and Frames?
> >
> > Sorry if this is obvious to everyone else, but I
think
> > I am a good test bed for those who want to know if
OO
> > people will move on to Frames...
> >
> > C
> >
> > On Fri, 08 Aug 2003 17:22:09 -0400, Leo Obrst wrote:
> >
> > >
> > > Hi, all,
> > >
> > > Sorry I've been removed from this discussion for
so
> > > long. I'd like to
> > > add my two cents here, tracing back on the
exchange
> of
> > > messages between
> > > Adam and Mike mostly.
> > >
> > > The whole distinction between frame and axiom
based
> > > systems comes down
> > > to this point:
> > >
> > > A frame system is object (meaning, entity)
centered.
> > > Axiomatic systems
> > > distribute the axioms that refer to those entities
> > (you
> > > can read
> > > "class", in general). So, frame systems bundle the
> set
> > > of
> > > assertions/axioms around an entity class.
Axiomatic
> > > systems do not.
> > >
> > > Are they equivalent logically: yes. View a frame
> > > assertion (typically
> > > depicted in Protege graphically, but in the output
> > > textually) as just a
> > > simple axiom.
> > >
> > > Axiom NOT EQUIVALENT TO rule. But axioms include
> rules
> > > (logical
> > > conditionals, biconditionals). Production rules
> > > (condition -> action)
> > > are a different story: they simulate logical
> > > implication and were
> > > predominant in the days of expert systems, when
> logic
> > > was not generally
> > > known and used among the various rule communities.
> > >
> > > The following can be axioms:
> > > (1)
> > > (Class Person) [or whatever syntax you like)
> > > (subClass Father Person) [these are not
necessarily
> > > correct sub-classes,
> > > but this is just for example purposes]
> > > (subClass Mother Person)
> > > (has (Class Person) (Property Birthdate)) [or
> > > "attribute" rather than
> > > property, depending on your KR language]
> > > ...
> > >
> > > (2)
> > > Frame systems in general have a built-in
> transitivity
> > > axiom that enables
> > > inheritance of properties down the privileged
> > taxonomic
> > > or "sub-class"
> > > relation (all OO systems implicitly have this
too):
> > >
> > > (2a) If B is an A, and C is an B, then C is an A.
> > >
> > > Also related to this is modus ponens reasoning:
If A
> > > has X, and B is an
> > > A, then B has an X. Another way of stating the
> latter
> > > is:
> > >
> > > (2b)
> > > If X then Y
> > > X
> > > ---- [conclude]
> > > Y
> > >
> > > These are all axioms. The (1) type axioms directly
> > > correspond to frame
> > > like assertions. The (2) axioms begin as inference
> > > rules, but once
> > > stated and proved (or just stated in the
definition
> of
> > > the axiomatic
> > > system), can be asserted as axioms.
> > >
> > > What does all of this mean: it really is a
> granularity
> > > issue in any
> > > given ontology system.
> > >
> > > Protege, because it is a frame system, does not
give
> > > ontology modeling
> > > folks the direct capability of expressing axioms.
> > > Instead, it (both as a
> > > tool and as an expression of an underlying
knowlege
> > > model/language, i.e.
> > > OKBC) does not carve out the knowledge
> representation
> > > space in the same
> > > set of constructs and instead parcels out the
> modeling
> > > constructs in
> > > terms of entity-oriented (OO-like) frames of
> > reference,
> > > where the frame
> > > acts as a container for all the assertions about
the
> > > particular class
> > > (except for built-ins special axioms like the
> > > inheritance/transitivity
> > > property of privileged "subclass" relations, which
> > > every OO system has).
> > >
> > > I hope this is clear. Please let me know if it's
> not,
> > > and I'll
> > > elaborate.
> > >
> > > Leo
> > >
> > > Ps. Here are some notes on frames from a course
I've
> > > taught, just for
> > > reference:
> > >
> > > - Frame-based systems are KR systems that use
frames
> > > - Introduced by Marvin Minsky (1975) to represent
> > > domain knowledge
> > > - Represent a stereotypical situation
> > > - Way of structuring knowledge
> > > - A network of nodes and relations
> > > - Generic (nonterminal) knowledge bottoming out
in
> > > instances
> > > (terminals)
> > > - The notion of a frame corresponds to early LISP
> > > programming language
> > > terminology: slot & filler, record-based,
> > defstruct-like
> > > - Frames represent Concepts, have additional
> > > information attached to
> > > them: definitional, how to use, etc-
> > > - In frame terminology, a concept is a Class, and
a
> > > relation is a Slot
> > > - Attributes (sometimes called properties) are
just
> > > slots defined on a
> > > domain (a specific class subtree) or one of its
> > > subdomains (a subclass
> > > of a domain class).
> > > - Frames Close to OO Paradigm
> > > - First formalized frame KR language: KL-1
> > > - Led to Description Logics
> > > - Bottom Line: Frames are equivalent to a Logical
> > > Representation
> > >
> > > - Frame Systems: ?object-oriented?
> > > - Centered around a ?frame? of reference, i.e.,
> > > class, not a
> > > predicate, as in logic
> > > - Constructs:
> > > - Frames
> > > - Taxonomies: isa/subclass
> > > - Multiple inheritance
> > > - Slots
> > > - Fillers
> > > - Facets
> > > - Description Logics are descendents of these,
> capture
> > > the declarative
> > > part of frames using a logic-based semantics
> > > - Most DLs are decidable fragments of FOL, are
very
> > > closely related to
> > > other formalisms such as modal logics & feature
> logics
> > > - DL classes (concepts) can be defined
intensionally
> > in
> > > terms of
> > > descriptions that specify the properties that
> objects
> > > must satisfy to
> > > belong to the concept
> > >
> > > - Knowledge Interchange Format (KIF): mostly FOL,
> but
> > > some 2nd Order
> > > - Purely a neutral language of interchange
> language,
> > > no inference
> > > engine
> > > - Has a LISP-like syntax
> > > - KIF very close to FOPC
> > > - Ontolingua built on KIF
> > > - Frame Ontology of KIF enables a frame-like
> > > representation of
> > > ontologies
> > > - OKBC (Open Knowledge Base Connectivity)
> language:
> > a
> > > declarative,
> > > knowledge base API for interconnecting KBs in
> > different
> > > KR
> > > representations
> > > - The basis for XOL (XML Ontology Interchange
> > > Language), based on
> > > ?OKBC-Lite?
> > > - XOL: the result of the study by the
> > > bioinformatics group (see,
> > > later)
> > > - OKBC roughly equivalent to KIF, but subset
> > >
> > >
> > > Adam Pease wrote:
> > > >
> > > > Mike,
> > > > My understanding is that first order logic
> > > completely subsumes frames
> > > > and description logics. So, nothing would be
lost
> > by
> > > choosing KIF.
> > > >
> > > > Adam
> > > >
> > > > At 11:00 AM 8/7/2003 -0400, MDaconta@xxxxxxx
> wrote:
> > > > >Hi Adam,
> > > > >
> > > > >I agree that the axioms are important to have.
Do
> > we
> > > lose any frame-based
> > > > >functionality in KIF?
> > > > >
> > > > >Also, as we go through this I would like us to
> > > continue to highlight
> > > > >differences between
> > > > >the approaches.
> > > > >
> > > > >Thanks,
> > > > >
> > > > >- Mike
> > > > >
> > > > >In a message dated 8/6/03 10:36:16 PM,
> > > adampease@xxxxxxxxxxxxx writes:
> > > > >> One can't just put off considering the
> axioms
> > > until later, because they
> > > > >>depend on the basic terms and relations. If
the
> > > terms and relations are
> > > > >>created in a limited frame language, it will
be
> > > make the axioms very hard
> > > > >>to state in a general way later.
> > > > >> If we agree that axioms are important to
> have
> > > (at some point in the
> > > > >>development process), then its important right
> now
> > > to create a
> > > > >>representation that will accommodate them
later.
> > > > >
> > > > >-------------------------------
> > > > >Michael C. Daconta
> > > > >Chief Scientist, APG, McDonald Bradley, Inc.
> > > > >www.daconta.net
> > > >
> > > >
> > >
> >
>
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> > > --
> > > _____________________________________________
> > > Dr. Leo Obrst The MITRE Corporation,
> Information
> > > Semantics
> > > lobrst@xxxxxxxxx Center for Innovative
Computing
> &
> > > Informatics
> > > Voice: 703-883-6770 7515 Colshire Drive, M/S H305
> > > Fax: 703-883-1379 McLean, VA 22102-7508, USA
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> --
> _____________________________________________
> Dr. Leo Obrst The MITRE Corporation, Information
> Semantics
> lobrst@xxxxxxxxx Center for Innovative Computing &
> Informatics
> Voice: 703-883-6770 7515 Colshire Drive, M/S H305
> Fax: 703-883-1379 McLean, VA 22102-7508, USA
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