Формальная философия 80, Зоран Огнянович, A Probabilistic Temporal Epistemic Logic

Abstract: After a short historical introduction to the field of probabilistic logic, I can talk about the recent papers - Zoran Ognjanović, Angelina Ilić Stepić, Aleksandar Perović, A Probabilistic Temporal Epistemic Logic: Strong Completeness, Logic Journal of the IGPL, 2022; - Zoran Ognjanović, Angelina Ilić Stepić, Aleksandar Perović, A probabilistic temporal epistemic logic: Decidability, Logic Journal of the IGPL, 2023; that offer a formalization of reasoning about distributed multi-agent systems. The papers give syntax and semantics of a propositional probabilistic temporal epistemic logic PTEL. The presented results are: soundness, strong completeness theorems and decidability. To illustrate expressiveness of PTEL we give a formal description of the Blockchain protocol. We also discuss how to extend PTEL to axiomatize the corresponding first-order logic.