query on petri nets & OOP

There may be a number of handwaving (and possibly incorrect) remarks in 
the following.

There is a correspondence between linear logic and Petri nets.  I am using 
the proofs as nets analogy.

Lafont's work also shows a semantical equivalence between closed symmetric
monoidal categories and linear logic. (also the work of Meseguer and Marti-Oliet)

Petri Nets have traditionally been considered as a model for representing conditional
and iterative behavior apart from representing true concurrency.  With the 
corelation between linear logic and Petri nets, does it mean that Petri nets can
represent other "functional programming or object-oriented programming" constructs
like power objects, inheritance, quantifiers and subtypes?

Any ideas would be most welcome.

Thanks in advance.

--Scott Aiyer

email: ...!uunet!well!aiyer