David, (01)
What John said is that A is a specialization of B if every axiom of B holds in
A, that is if a population that satisfies A always satisfies B. For the
ontology containing only these predicates, we have no easy way to know what
satisfying these axioms might be. If we take these terms to mean what we
expect, then, as you point out, the ENTERPRISE ontology specializes the ACME
ontology, with the mapping you give (where saying MaritalStatus.Unknown(x) is
maps to Exists(x)). And the two parties can work together with only the
concepts in the ACME ontology. It is not necessary to map ACME knowledge to
the Enterprise predicates, since they are not part of the shared ontology.
Enterprise need not have an equivalent term for Single(x), they only need to be
able to phrase the ACME axioms for Single(x). It may be as simple as
understanding (not (Married x)), and certain implications thereof. (02)
The real problem is that organizations typically cannot be satisfied with the
common ontology. Their systems require population of certain information, and
if that information is not in the shared ontology, the systems don't work.
What that means is that the *required common ontology* for the joint action
that brings them together is in fact a specialization of the one they actually
share, and they don't share that specialization. (03)
-Ed (04)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of David Whitten
> Sent: Friday, September 19, 2014 10:53 AM
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] Generalization, specialization, and
> interoperability
>
> I wish that real systems matched some of the mathematical elegance that
> John Sowa's detailed note displayed.
>
> To elaborate a little on the real world interoperability issues, I have
> addressed, please look at a single property of a Person to denote the status
> of marriage for an individual.
>
> On one system (let's call it ACME), there is a property named MARRIAGE
> STATUS with the following values:
> MARRIED
> SINGLE
>
> on another system (let's call it ENTERPRISE), there is a property named
> MARITAL STATUS with the following values:
> DIVORCED
> MARRIED
> NEVER MARRIED
> SEPARATED
> UNKNOWN
> WIDOWED
>
> On the face of it, these are both compatible, but in actuality there is only
> easy interoperability in one direction, from ENTERPRISE to ACME, but not
> from ACME to ENTERPRISE.
>
> ENTERPRISE -> ACME
>
> DIVORCED -> SINGLE
> MARRIED -> MARRIED
> NEVER MARRIED -> SINGLE
> SEPARATED -> MARRIED
> UNKNOWN -> ????
> WIDOWED -> SINGLE
>
> If the ACME system can not store an answer to this property, the UNKNOWN
> case can just be ignored by not storing any answer.
>
> The opposite direction (from ACME to ENTERPRISE) is fraught with arbitrary
> solutions.
>
> Perhaps the real problem is that even with this (real) example, there is the
> built-in 3D mind set that says what is stored in the system right now is true
> since the last change. This formulation doesn't have the idea of a date of
> transition (Wedding Date, Death Date of Spouse, Divorce Date, Separation
> Date) or that this concept of Status_of_Marriage is actually not static at all
> but is fluid.
>
> David Whitten
> 713-870-3834
>
>
> On Fri, Sep 19, 2014 at 10:15 AM, John F Sowa <sowa@xxxxxxxxxxx> wrote:
> > In another forum, I sent a note about using the terms 'generalization'
> > and 'specialization' as a way to clarify relationships among
> > ontologies (or any theories of any kind).
> >
> > In particular, they provide a convenient way to specify the conditions
> > for interoperability among theories and the systems they describe:
> >
> > 1. Definition. A theory A is a generalization of a theory B iff B
> > entails A: every model for which B is true is also a model for A.
> > If A is a generalization of B, then B is a specialization of A.
> >
> > 2. Even when those two words aren't used, the concept is implicit.
> > In Cyc, for example, they are the basis for the partial ordering
> > of microtheories: every microtheory is a specialization of
> > (entails) the theories above it in the hierarchy.
> >
> > 3. As another example, Schema.org is a very general (underspecified)
> > collection of types (or classes) that many developers adopted for
> > applications that are inconsistent with one another. But the
> > theories that specify those applications (explicitly or implicitly)
> > are all specializations of Schema.org.
> >
> > 4. If data d is specified in a general theory, such as Schema.org, and
> > used a more specialized theory X, all properties of d specified in
> > the general theory may be assumed in X. But any property P that
> > is not specified in the general theory may be used in X only after
> > a test such as "If P(d), then ..."
> >
> > 5. With these two terms, the conditions for interoperability among
> > two theories A and B (or any systems that are specified by or
> > described by A and B) can be stated:
> >
> > a) If two theories A and B are inconsistent in their details,
> > they can interoperate on shared data that is specified by
> > a common generalization C.
> >
> > b) To use data specified in C, neither A nor B may assume any
> > properties of that data not specified in C. But they can use
> > the details in conditionals that begin "If x has property P ..."
> >
> > c) Points 5a and 5b are implicit in the way interoperable systems
> > work. The spec's for the data on which interoperability is
> > required are the common generalization C. Any property not
> > specified in C can only be used in A or B after an appropriate
> > test.
> >
> > The generalization/specialization distinction can also clarify other
> > relationships, practical and theoretical. For example, we have often
> > discussed issues about defaults, open worlds vs close worlds, and
> > related problems in nonmonotonic reasoning.
> >
> > But every proof in a nonmonotonic logic can be converted to a proof in
> > a monotonic (classical) logic from a suitably revised theory --
> > because each nonmon step adds, deletes, or modifies a monotonic axiom.
> >
> > After the nonmon proof has finished, it's possible to gather up all
> > the monotonic axioms into one purely classical theory, from which an
> > equivalent proof can be carried out with classical rules of inference.
> >
> > In terms of generalization/specialization, every nonmon proof
> > corresponds to a walk in a lattice of classical theories. The full
> > lattice may be infinite, but only a finite set of nodes are used for
> > any application: The number of nodes is equal to the number of steps
> > in the nonmon proof.
> >
> > Summary: The terms 'generalization' and 'specialization' can be used
> > to explain and clarify a wide range of issues, both practical and
> > theoretical.
> >
> > John
> >
> >
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