Starting off with Moss and Parikh’s investigation into knowledge and topology, we propose a logical system which is capable of formally handling endomorphisms of subset spaces. The motivation for doing so originates from dynamic agent logics. Usually, these logics comprise certain epistemic actions. Our aim is to show that an appropriate extension of the Moss-Parikh system can serve similar purposes. In fact, since the semantics of an action can be described as a function inducing a change of the knowledge states of the involved agents, such transformations are to be modeled accordingly. Due to the ambivalence of the framework used here, this has some quasi-topological impact, too, in so far as a certain notion of open mapping can be captured now. The main issues of this paper concern the basic logical properties of the arising system, in particular, completeness. Our main technical resource for that is hybrid logic.
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