  In this paper we provide a first-ever epistemic formulation of stabilizing
agreement, defined as the non-terminating variant of the well established
consensus problem. In stabilizing agreements, agents are given (possibly
different) initial values, with the goal to eventually always decide on the
same value. While agents are allowed to change their decisions finitely often,
they are required to agree on the same value eventually. We capture these
properties in temporal epistemic logic and we use the Runs and Systems
framework to formally reason about stabilizing agreement problems. We then
epistemically formalize the conditions for solving stabilizing agreement, and
identify the knowledge that the agents acquire during any execution to choose a
particular value under our system assumptions. This first formalization of a
sufficient condition for solving stabilizing agreement sets the stage for a
planned necessary and sufficient epistemic characterization of stabilizing
agreement.
