Ian, (01)
All those things were precisely defined in logic a century ago,
and it would be a simple exercise to map the axioms to CL. (02)
IB> I think IDEAS could be mapped to CL, we've just had no cause
> to do it. We'd have to find some CLudge for representing the
> higher-order aspects (powersets, sets of tuples, sets of sets,
> ... even sets of type-instance tuples are possible in IDEAS). (03)
The Z notation (which I admit is one of the most unreadable)
can be easily mapped to CL. Furthermore, the Z mathematical
toolkit, which is part of the ISO standard for Z, defines all
those aspects plus a lot more. (04)
CL + Z toolkit is not a kludge, and the horrible symbols of Z
can be mapped to more readable words in CL or Controlled English.
In fact, the full CL semantics can be expressed in Controlled
English. That is the point of my slides: (05)
http://www.jfsowa.com/talks/cnl4ss.pdf (06)
And as Chris Menzel said, CL does support what many people
call higher-order logic. In fact, it includes the logic
used by the system named HOL (for Higher-Order Logic). (07)
IB> I think IDEAS could be mapped to CL, we've just had no cause
> to do it. (08)
That is what the "Three Amigos" who defined UML said. Following
is an excerpt from Wikipedia: (09)
W> In 1996 Rational concluded that the abundance of modeling
> languages was slowing the adoption of object technology, so
> repositioning the work on a unified method, they tasked the
> Three Amigos with the development of a non-proprietary
> Unified Modeling Language. Representatives of competing object
> technology companies were consulted during OOPSLA '96; they
> chose boxes for representing classes over Grady Booch's Booch
> method's notation that used cloud symbols. (010)
Note that a logical foundation was far lower on their list
of priorities than the choice of boxes vs. clouds. (011)
W> The use case notation from Objectory and the component notation
> from Booch were integrated with the rest of the notation, but
> the semantic integration was relatively weak in UML 1.1, and was
> not really fixed until the UML 2.0 major revision. (012)
UML 2.0 is indeed much better defined. But note the following: (013)
W> ... the OMG provides no test suite to objectively test compliance
> with its specifications. (014)
John (015)
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