Leo, (01)
I've been looking closely at OWL these days. Given the points of view
you express here, could you comment on the, shall I call it, expressive
power of OWL in terms of, say, axoimatic systems? (02)
Thanks
Jack (03)
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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> (05)
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