Goal specification using temporal logic in presence of non-deterministic actions

In this paper we show that despite a past claim goals such as ‘try your best to make p true’ in presence of non-deterministic actions can be expressed in the framework of branching time temporal logic. We analyze the A and E operators in CTL∗ and point out why it was thought that the above mentioned goal can not be expressed using CTL∗. We then introduce the operators Aπ and Eπ (and present a temporal logic π-CTL∗) which take into account the policy being followed by the agent and show that using these operators we can indeed specify the above mentioned goal.