Modal Logics of Reactive Frames

A reactive graph generalizes the concept of a graph by making it dynamic, in
the sense that the arrows coming out from a point depend on how we got there.
This idea was
fi
rst applied to Kripke semantics of modal logic in [2]. In this
paper we strengthen that unimodal language by adding a second operator. One op-
erator corresponds to the dynamics relation and the other one relates paths with the
same endpoint. We explore the expressivity of this interpretation by axiomatizing
some natural subclasses of reactive frames.
The main objective of this paper is to present a methodology to study reactive
logics using the existent classic techniques.