How to Do Social Simulation in Logic: Modelling the Segregation Game in a Dynamic Logic of Assignments

The aim of this paper is to show how to do social simulation in logic. In order to meet this objective we present a dynamic logic with assignments, tests, sequential and nondeterministic composition, and bounded and non-bounded iteration. We show that our logic allows to represent and reason about a paradigmatic example of social simulation: Schelling’s segregation game. We also build a bridge between social simulation and planning. In particular, we show that the problem of checking whether a given property P (such as segregation) will emerge after n simulation moves is nothing but the planning problem with horizon n, which is widely studied in AI: the problem of verifying whether there exists a plan of length at most n ensuring that a given goal will be achieved.