  Understanding a \textit{reinforcement learning} policy, which guides
state-to-action mappings to maximize rewards, necessitates an accompanying
explanation for human comprehension. In this paper, we introduce a set of
\textit{linear temporal logic} (LTL) formulae designed to provide explanations
for policies, and an algorithm for searching through those formulae for the one
that best explains a given policy. Our focus is on crafting explanations that
elucidate both the ultimate objectives accomplished by the policy and the
prerequisite conditions it upholds throughout its execution. These LTL-based
explanations feature a structured representation, which is particularly
well-suited for local-search techniques. The effectiveness of our proposed
approach is illustrated through a simulated game of capture the flag and a
car-parking environment. The paper concludes with suggested directions for
future
