Abstract
The modal characterization theorem by J. van Benthem characterizes classical modal logic as the bisimulation invariant fragment of first-order logic. In this paper, we prove a similar characterization theorem for intuitionistic modal logic. For this purpose we introduce the notion of modal asimulation as an analogue of bisimulations. The paper treats four different fragments of first-order logic induced by their respective versions of Kripke-style semantics for modal intuitionistic logic. It is shown further that this characterization can be easily carried over to arbitrary first-order definable subclasses of classical first-order models.
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