See my comments inline below. (01)
-- Ken (02)
On Fri, 21 Mar 2008, John F. Sowa wrote: (03)
> Pat and Barry,
>
> Some comments on the issue of multilingual support.
>
> JFS>> The stated goal of Common Logic was to avoid or at least mitigate
> >> such [syntactic] controversies by using an *abstract syntax* that
> >> brings a large number of concrete syntaxes under a common semantic
> >> umbrella.
>
> BS> No disagreement here.
>
> Good. I'm happy to find an important area of agreement.
>
> PH> A multilingual repository would be a lot more useful if it came
> > with recommended ways to translate between the languages. For OWL
> > and FOL/CL this is now thoroughly understood, for example.
>
> I agree. But I would make the point stronger by claiming that
> such translations are more than useful -- they're a prerequisite
> for a multilingual repository.
>
> PH> One can define a sublanguage of CLIF which is virtually isomorphic
> > to the OWL abstract syntax. If I ever get time (in a month or so,
> > maybe) I will write this up in detail as an alternative OWL syntax.
>
> That would be an excellent exercise, which would be of enormous
> interest to everybody. I hope you can get at least a sketch of it
> done soon.
>
> PH> For things like UML it is much more problematic, as there is not
> > even a common underlying semantic framework within which to compare
> > such notations with logics.
>
> That issue is complicated by various trends within the UML community.
> Some of the UML supporters suggested and developed various logical
> foundations for years, but others have been pushing UML toward a
> more procedural approach.
>
> As one example of a logic-based approach, there is a group called
> PUML (Precise UML) that has been defining the UML diagtrams in Z.
> See the excerpts below. There's another group, called F-UML,
> that has been defining UML in Object Z. There's also an approach
> based on category theory:
>
> http://www1.coe.neu.edu/~jsmith/Publications/ecoop.pdf (04)
Unfortunately, that link is broken. Here is a better link: (05)
http://www.ccs.neu.edu/home/kenb/pub/2000/03/public.pdf (06)
This paper gives an overview of some of the category theoretic approaches
to formalizing UML developed by my colleagues and me at Northeastern
University. However, we use category theory only as a means of
integrating (fusing) FOL theories. We did not introduce a new kind of
theory or semantics. The various UML diagrams for a project can represent
different aspects (e.g., class diagrams vs. activity diagrams) of the
project or can view the project at different granularities (e.g., use case
diagrams vs. class diagrams). Theory morphisms can be used for mapping
one ontology to another, and colimits can be used to merge ontologies that
overlap one another (e.g., use the same upper ontology). (07)
For more recent research on this approach to ontology mapping and
modularity, see the excellent presentation by John Bateman back in
January: (08)
http://ontolog.cim3.net/cgi-bin/wiki.pl?ConferenceCall_2008_01_31 (09)
Since ontology mapping and merging are problems that OOR users will need
to address, category theoretic approaches should be reviewed at the
Ontology Summit 2008. (010)
> This abundance of approaches is discouraging because it implies
> that none of them has reached a critical mass of support. My
> recommended approach would be simpler:
>
> 1. Don't wait for the UML community to do anything.
>
> 2. Don't attempt to define all the UML diagrams formally.
>
> 3. Instead, use a subset of the UML diagramming conventions
> for which the mapping to Common Logic is obvious.
>
> 4. Supplement the diagrams with a version of controlled English
> that maps to full CL (an example is CLCE -- Common Logic
> Controlled English -- but other notations such as ACE would
> be quite acceptable.)
>
> 5. If anybody wants to do full UML, encourage them, but don't
> hold your breath waiting. (011)
Would Evan Wallace or Elisa Kendall care to comment on this? (012)
-- Ken (013)
>
> John
> _________________________________________________________________________
>
> Source: http://www4.informatik.tu-muenchen.de/publ/papers/EFLR98b.pdf
>
> Developing the UML as a Formal Modelling Notation
>
> A. Evans, R. France, K. Lano, B. Rumpe
>
> Abstract
>
> The Unified Modeling Language (UML) is rapidly emerging as a de-facto
> standard for
> modelling OO systems. Given this role, it is imperative that the UML
> have a well-defined,
> fully explored semantics. Such semantics is required in order to ensure that
> UML concepts are precisely stated and defined. In this paper we describe and
> motivate an approach to formalizing UML in which formal specification
> techniques
> are used to gain insight into the semantics of UML notations and
> diagrams. We
> present work carried out by the Precise UML (PUML) group on the
> development of a
> precise semantic model for UML class diagrams. The semantic model is
> used as the
> basis for a set of diagrammatical transformation rules, which enable formal
> deductions to be made about UML class diagrams. It is also shown how
> these rules
> can be used to verify whether one class diagram is a valid refinement
> (design) of
> another. Because these rules are presented at the diagrammatical level,
> it will be
> argued that UML can be successfully used as a formal modelling tool
> without the
> notational complexities that are commonly found in formal specification
> techniques.
>
> 5. Summary and Open Issues
>
> In this paper we outlined and illustrated an approach to formalizing the
> UML.
> The objective of our efforts is to make the UML itself a precise
> modelling notation so
> that it can be used as the basis for a rigorous software development
> method. However,
> it must first be determined how such a formalization can best be carried
> out, and what
> practical purpose it can serve. This paper aims to contribute to this
> ongoing
> discussion.
>
> The benefits of formalization can be summarized as follows:
>
> ? Lead to a deeper understanding of OO concepts, which in turn can lead
> to more mature use of technologies.
>
> ? The UML models become amenable to rigorous analysis. For example,
> rigorous consistency checks within and across models can be supported.
>
> ? Rigorous refinement techniques can be developed.
>
> An interesting avenue to explore is the impact a formalized UML can have
> on OO
> design patterns and on the development of rigorous domain-specific software
> development notations. Domain-specific UML patterns can be used to bring UML
> notations closer to a user's real-world constructs. Such patterns can
> ease the task of
> creating, reading, and analyzing models of software requirements and
> designs.
> An integrated approach to formalization of UML models is needed in order
> to provide
> a practical means of analyzing these models. Current work on compositional
> semantics [1] has used techniques for theory composition to combine semantic
> interpretations of different parts of an OO model set.
>
>
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