Reasoning about Belief in Social Software using Modal Logic

Social software is the interdisciplinary research program in which social procedures are analyzed and designed using formal, mathematical methods. The analysis of certain procedures requires explicit mention of belief. We develop a logic, based on propositional dynamic logic, that allows us to explicitly reason about belief in social software. This logic consists of a static logic, and dynamic updates. We show how this logic can be used by analyzing the example in which a bank can go bankrupt only because of clients’ beliefs. We also give a complete axiomatization of the static logic, and we show (analogously to [vBvEK] and [vEW]) how the updates can be reduced to the static logic. Moreover, we implement model checking software for our logic. Finally, we give suggestions as to what purposes our logic can be used as well.