Decision-Making Under Uncertainty: Beyond Probabilities

This position paper reflects on the state-of-the-art in decision-making under uncertainty. A classical assumption is that probabilities can sufficiently capture all uncertainty in a system. In this paper, the focus is on the uncertainty that goes beyond this classical interpretation, particularly by employing a clear distinction between aleatoric and epistemic uncertainty. The paper features an overview of Markov decision processes (MDPs) and extensions to account for partial observability and adversarial behavior. These models sufficiently capture aleatoric uncertainty but fail to account for epistemic uncertainty robustly. Consequently, we present a thorough overview of so-called uncertainty models that exhibit uncertainty in a more robust interpretation. We show several solution techniques for both discrete and continuous models, ranging from formal verification, over control-based abstractions, to reinforcement learning. As an integral part of this paper, we list and discuss several key challenges that arise when dealing with rich types of uncertainty in a model-based fashion

Characterizing perfect recall using next-step temporal operators in S5 and sub-S5 Epistemic Temporal Logic

We review the notion of perfect recall in the literature on interpreted systems, game theory, and epistemic logic. In the context of Epistemic Temporal Logic (ETL), we give a (to our knowledge) novel frame condition for perfect recall, which is local and can straightforwardly be translated to a defining formula in a language that only has next-step temporal operators. This frame condition also gives rise to a complete axiomatization for S5 ETL frames with perfect recall. We then consider how to extend and consolidate the notion of perfect recall in sub-S5 settings, where the various notions discussed are no longer equivalent