Hi, all, (01)
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. (02)
The whole distinction between frame and axiom based systems comes down
to this point: (03)
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. (04)
Are they equivalent logically: yes. View a frame assertion (typically
depicted in Protege graphically, but in the output textually) as just a
simple axiom. (05)
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. (06)
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]
... (07)
(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): (08)
(2a) If B is an A, and C is an B, then C is an A. (09)
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: (010)
(2b)
If X then Y
X
---- [conclude]
Y (011)
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. (012)
What does all of this mean: it really is a granularity issue in any
given ontology system. (013)
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). (014)
I hope this is clear. Please let me know if it's not, and I'll
elaborate. (015)
Leo (016)
Ps. Here are some notes on frames from a course I've taught, just for
reference: (017)
- 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 (018)
- 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 (019)
- 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 (020)
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
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