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isa and hasa in UML

From: Francis McCabe <fgm@fla.fujitsu.com>
Date: Fri, 30 May 2003 10:00:38 -0700
To: www-ws-arch@w3.org
Message-Id: <3CB0C811-92C0-11D7-BA7E-000393A3327C@fla.fujitsu.com>

This is in partial fulfillment of my action item re is-a and has-a 
w.r.t. UML

0. There is a rather (unintentionally) funny comment in the UML 2.0 
spec:

2.3.2.3 Semantics
   The meanings of the constructs are defined using natural language. ...

(This is after a lot of promises of being formal.)

   However, UML uses OCL for those cases where natural language is not 
enough. OCL is similar to a first order predicate calculus. Having said 
that, the spec does not use OCL very often; including for the 
definition of relationships such as generalization (is-a) and 
association (has-a kind of)

1. As I have indicated earlier, UML does not have a precise notion of 
is-a. The closest is the generalization relationship. This is defined 
in 3.50:

Generalization is the taxonomic relationship between a more general 
element and a more specific element that is fully consistent and that 
adds additional information.

A couple of comments:

1. Basing is-a on taxonomics raises some serious logical issues. This 
is analogous to basing everything on sets: every member of the penguin 
set is also a member of the bird set.

The problem is that it becomes really difficult to talk about weird or 
abstract sets. Basing is-a on this would lead to the following 
counter-intuitive result: every unicorn is a yeti. (There are no 
documented instances of either, so the set of unicorns and yetis is 
indistinguishable.)

A more serious issue, sticking with birds for the moment, is that it is 
similarly hard to talk about properties of birds such as flying: we 
could not express the fact that all birds except penguins fly.

An even more serious issue is that we need to capture the following 
situation:

A service has an identifier

A Web service is a service
A Web service has a URI

The Web service's URI counts_as the service identifier

It is that counts_as that is beyond the capabilities of UML's 
generalization. We *could* extend UML's generalization, and that may be 
the best overall approach. In fact, we would really need to do that for 
all our relationships, use is-a and has-a and *never* rely on UML's 
built-in relationships. is-a and has-a could probably be defined in 
OCL.


More to follow....
Frank
Received on Friday, 30 May 2003 13:01:46 GMT

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