Help with UML needed (sic)

[Frank McCabe <frank.mccabe@us.fujitsu.com>]

I am fairly sure that this diagram:

is not 'proper' UML. So I am looking for help here ...

Here is what I am trying to say:

Policies, and needs are both sub-types of Proposition. (We can argue  
whether that is in fact the case, but that is beside the point here.  
Certainly there is more to both than I am modeling right now)

Similarly, both the shared state and the private state are composed  
of (aggregates of) propositions. Again, technically, there is more to  
state than this. What I am trying to say here is that state is  
characterized by assertions, which are propositions. I also need  
commitments... which are propositions about the future.

A proposition has an attribute that it is measurable. It also has  
attributes such as the notation of the prop and the domain of the prop.

A need is a proposition whose domain is in the set of propositions  
that are in the shared state (and in the private state as I want to  
capture here).

So, my questions are, have I used UML correctly (probably not) and  
how should one capture the above intuition?

I enclose a magicdraw file for the adventurous...

Participant Model.mdxml

Frank