Probabilistic Obstruction Temporal Logic: a Probabilistic Logic to Reason about Dynamic Models

Abstract: In this paper, we propose a novel formalism called Probabilistic Obstruction Temporal Logic (POTL), which extends Obstruction Logic (OL) by incorporating probabilistic elements. POTL provides a robust framework for reasoning about the probabilistic behaviors and strategic interactions between attackers and defenders in environments where probabilistic events influence outcomes. We explore the model checking complexity of POTL and demonstrate that it is not higher than that of Probabilistic Computation Tree Logic (PCTL), making it both expressive and computationally feasible for cybersecurity and privacy applications.