Abstract
Hennessy and Milner have shown that observational equivalence can be characterized by a modal language. We show here that a subset of this language, without an explicit negation operator, also characterizes it. Using this subset we offer sound and complete modal proof systems for simple nondeterministic languages of processes. In the case where observational equivalence is not a congruence we show that the observational congruence can also be characterized modally. Using this new language we again offer a sound and complete proof system. We briefly comment upon proof systems for extensions of the nondeterministic process languages.
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