Hello,

I'm writing a work and I do not really know which is the best way to specify the following transformation function. Let me introduce it by a simple example.

Let us supose that we have defined a tuple of objets and relationships at a given moment :

the set of objects is , where:

and the relationships are

Given an initial tuple at moment , I want to define a transformation function . This function consists in applying the required changes (in terms of addition or deletion) in order to obtain an specific tuple at moment . That is, let us supose that the tuple that is wanted to be reached at moment is the following:

, where:

Then, in order toobtainthe final tuple from the initial tuple, we require toapplya set of changes :

and here is when I don't know which is the best way to say the next:

A transformation function defines how a given tuple at a initial moment, can be transformed into another tuple at a final moment, that is, the changes that must be applied to the initial tuple at moment in order to obtain the final tuple at moment :

But I think this is not correct,may be better in the following way??

or this one??:

---------------------------------------------------------------------------

Now let us supose that the relationship consists on a function between a pair of objects such that, if returns 0 means that the person does not drive the car, if returns 1, the person drives the car:

If I write this relationship in this way, I could say that a change of addition means that the funcion returns 1 and a change of deletion means that the function returns 0??How I should specify this??

May I use the same notation than the first one?? I mean, may I say that exists a set of changes , such that, when applied to the initial tuple we obtain the final one??

If this is correct, how I could write that a change of addition between a pair of objects and means that and a change of deletion means that ??

How could I write this??

That's all. If someone could help me I would be very grateful

Thank you.