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We are concerned with the problem of defining a complex, hybrid, agent based discrete system in a modular way. The modularity results from looking at the system from a numbci of different perspectives, each dealing with a specific aspect of the system. As a solution a synchronisation operator is proposed which glues agent aware systems on shared agents and transitions. The construction turns out to...
It has been observed that various synchronisation operators that underly modular design of concurrent systems can be explained as {\em pullbacks in suitable categories of concurrent systems. Here, the boundaries of such approach are investigated. For this purpose we study the issue of completeness in categories of trace monoids. It turns out that (finite) completeness is achieved if trace monoids...
A logic LP= for reasoning about change is presented. The logic, an extension of the logic of ó predicates with equalitu, is based on the idea that explicit substitutions can be seen as atomic formulae describing basic change of the state of a system. The logic is substructural: non-monotone and non-commutative. Its Platonic, i.e., predicate part is governed by the additive connectives, while the identity...
A new notion of a general morphism of Petri nets is introduced. The new morphisms are shown to properly include the morphisms considered so far. The resulting category of general Petri nets is shown to admit products. Here, it is shown that the new notion turns out to be indispensable to facilitate functoriality of synthesis of transition systems by means of (labelled) state machines. In the companion...
The menagerie of epimorphisms in the category Cat of small categories is studied. The standard notion of a congruence on a category is generalized and used subsequently to introduce the notion of a kernel of a functor, quotient category and quotient functor. Theory of concurrent processes seems to be a natural place to look for applications of the notions and results presented here in the area of...
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