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Bisimulations and predicate logic. (English) Zbl 0809.03018
First, some basic results concerning the coinductive characterization of bisimilarity are presented. It is proved that bisimilarity is not preserved under elementary substructures and it is analyzed how certain transitions defined from data models depend on data by turning a bisimulation into an isomorphism between the data models. The data dependence of transitions is shown to be first-order by internalizing nondeterminism in states given as sets. Further, bisimulation is studied as an extensional notion of equivalence on programs, generalizing input/output equivalence (a $$\Pi^ 0_ 2$$-notion), an equivalence that may fall outside of $$\Pi^ 1_ 1$$. This explosion in logical complexity is a measure of the scope of bisimilarity resting heavily on infinite branching.

##### MSC:
 03B70 Logic in computer science 68Q55 Semantics in the theory of computing
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