Modularity and expressibility for nets of relations

Modularity reflects the Frege Principle: any two expressions expr₁ and expr₂ which have the same meaning (semantics) can be replaced by each other in every appropriate context C[ ] without changing the meaning of the overall expression. In [18] we identified observable relations and nets of observable relations as appropriate tools for the investigation of dataflow networks over nondeterministic agents. The observable relations are the Input-Output behaviors of (in general nondeterministic) dataflow agents. Moreover, the semantics of nets of observable relations is consistent with the input-output behavior of dataflow agents. In [18, 19] we showed that the main source of the Brock-Ackerman anomaly [2] is in the semantics of nets of relations. But it turns out that this semantics is not modular. The central objective of this paper is the characterization of modular classes of relations and hence indirectly the set of dataflow nets without anomalies. Another major theme which plays a technical role in this characterization, but is interesting in its own, is the expressibility for relational nets. The investigation also reveals the interesting role played by stable functions introduced by Berry [3].