Towards a Calculus for Nondeterministic Schemas in Z

In our previous work, we presented a Z-based formalism, called NZ, by which one can explicitly specify bounded, unbounded, erratic, angelic, demonic, loose, strict, singular, and plural nondeterminism. The NZ notation is mainly based on a new notion of operation schemas, called multi-schema. Since the operations of the Z schema calculus do not work on multi-schemas anymore, in this paper we augment NZ with a new set of schema calculus operations that can be applied on multi-schemas as well as ordinary operation schemas. To demonstrate the usability of the resulting formalism, we show how this formalism can assist to model game-like situations and concurrent systems as two well-known classes of nondeterministic systems.