From: Ken Baclawski (kenb@ccs.neu.edu)
Date: 01/26/01
I think we are generally in agreement also. I agree that it is desirable to achieve transformations with this property. Our only disagreement may be in how difficult it is to ensure this property. To see why, suppose that we have transformations U2D and D2U such that for any UML class diagram x, U2D(D2U(U2D(x))) = U2D(x). Then the function f defined by f(x) = D2U(U2D(x)) is a closure operator on the set of all UML class diagrams. A closure operator in this case would mean that the transformations U2D and D2U can be used to construct a "canonical form" for UML class diagrams relative to DAML (and vice-versa). While canonical forms are nice, in practice it is difficult to define them. -- Ken On Fri, 26 Jan 2001, Hart, Lewis wrote: > I believe we are generally in agreement. Just to clarify a bit, let me say > that the ultimately the transformations between UML and DAML should be > constrained sufficiently so that they are bounded for a limited subset of > UML and DAML. That is, the middle part in the "figure" below. > > [Full UML] -- U2D --> [sub DAML] < -- U2D/D2U --> [sub UML] <-- D2U -- [Full > DAML] > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ > The tricky bit is to make the set of transformations as large as possible > and the limitations as small as possible in order to maximize utility of the > process. > > - Lewis. > _____________________________________________________ > Lewis L Hart > GRC International lhart@grci.com > 1900 Gallows Rd. Voice (703)506-5938 > Vienna, Va 22182 Fax (703)556-4261 > > -----Original Message----- > From: Ken Baclawski [mailto:kenb@ccs.neu.edu] > Sent: Friday, January 26, 2001 12:49 AM > To: Hart, Lewis > Cc: daml-graphical@mail.daml.org > Subject: RE: revised UML profile for DAML > > On Wed, 24 Jan 2001, Hart, Lewis wrote: > > > The mapping which I have posted is primarily for UML to DAML. This > mappings > > is many to one, that is there are several UML situations which are mapped > > into the single DAML Property. Typical of a many to one mapping, the > inverse > > mapping looses some information. For a given DAML property, it is not > > apparent from the DAML alone what UML elements resulted in that property. > > Clearly, the reverse mapping is free to pick any one of the UML > > representations that are semantically equivalent. The I believe this > > prevents the unbounded situation, though the UML representation will not > be > > identical. > > Yes, this is the usual situation. Both the UML -> DAML mapping and the > DAML -> UML mapping will be many to one. However, even if they preserve > semantics, the pair of mappings can still be unbounded. The example of ER > -> Relational and Relational -> ER that I mentioned in an earlier posting > preserves semantics, but it is still unbounded. > > > Consider the "child" and "mother" roles of the "Parent" association found > at > > link [1], and shown crudely below. Starting from one UML binary > association > > with two roles: > > > > child mother > > [Person] -------- Parent> -------------[Woman] > > > > it is mapped/transformed into three DAML properties(ignoring cardinality, > > domain and range): > > > > <Property id="child"/> > > <Property id="mother"> > > <subPropertyOf resource = "Parent"/> > > </Property> > > <Property id="Parent"/> > > > > The inverse transformation could result in three associations without > roles > > and a generalization between stereotyped classes: > > > > [ ] -----------mother> ---------- [ ] > > [person] ---------- Parent> ---------- [Woman] > > [ ] --------- <child ------------ [ ] > > > > [<<Property>>] [<<Property>>] > > [ mother ] ---- generalization > ---- [ Parent ] > > > > I do not see how this results in an unbounded situation, since both of > these > > UML representations result in identical DAML when transformed. > > > > Furthermore, I think it is unreasonable for UML<->DAML transformations to > be > > totally reversible. That is, if UML1 is transformed into DAML1 and then > back > > to UML2, then UML1 will be not identical to UML2. What I believe should > > be true is that if the transform is applied again to UML2 to produce > > DAML2, then DAML1 and DAML2 should be identical. This defines semantic > > equivalence for UML models with respect to DAML. > > My formulation of the problem did not presume that the transformations > were invertible, and I agree that it is unreasonable to expect > transformations to have this property. However, one must expect that both > transformations (UML -> DAML and DAML -> UML) will "lose information", not > just UML -> DAML. So it may be difficult to achieve convergence as > quickly as you propose. Nevertheless, it is certainly reasonable to > propose that this be one of the goals of the UML -> DAML transformation > effort. > > -- Ken Baclawski >
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