A probabilistic temporal epistemic logic: Strong completeness

Abstract

The paper offers a formalization of reasoning about distributed multi-agent systems. The presented propositional probabilistic temporal epistemic logic PTEL is developed in full detail: syntax, semantics, soundness and strong completeness theorems. As an example, we prove consistency of the blockchain protocol with respect to the given set of axioms expressed in the formal language of the logic. We explain how to extend PTEL to axiomatize the corresponding first-order logic.