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A language for specifying nondeterministic operations which generalizes the equational specification language is introduced. Then, various notions of generated multimodels are discussed and sufficient conditions for the existence of quasi-initial semantics of nondeterministic specifications are given. Two calculi are introduced: NEQ and NIP. The former is sound and complete with respect to the class of all multimodels. The latter is an extension of the former with the -rule. It is sound and complete with respect to one of the classes of the generated multimodels. The calculi reduce to the respective deterministic calculi whenever the specification involves only deterministic operations.

Generated models and the ω-rule: The nondeterministic case