Goal specification using temporal logic in presence of non-deterministic actions Chitta Baral Matt Barry Department of Computer Sc. and Engg. Advance Tech Development Lab Arizona State University United Space Alliance Tempe, Arizona 85287 Houston, TX 77058 chitta@asu.edu Matthew.R.Barry@USAHQ.UnitedSpaceAlliance.com Abstract 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 A π and E π (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. 1 Introduction and motivation ❤ ▲ ▲ ▲ STORE SW LAB NE DEP robot Figure 1: A navigation domain In recent years it has been proposed [Bacchus and Kabanza, 1998; Niyogi and Sarkar, 2000; Pistore and Traverso, 2001; Baral et al., 2001] that temporal logic be used to specify goals that go beyond only putting conditions on the final state. Most of these papers – except [Pistore and Traverso, 2001], only consider the case when actions are determinis- tic. In [Dal Lago et al., 2002] it is argued that in presence of non-deterministic actions 1 certain kind of goals can not be expressed using temporal logic and an alternative language to specify goals is crafted. In this paper we counter this claim and show that some of the goals discussed there can indeed be expressed using temporal logic if we define the operators appropriately. To motivate the difficulties associated with goal specification in presence of non-deterministic actions we start with the fol- lowing example from [Dal Lago et al., 2002]. ✫✪ ✬✩ ✫✪ ✬✩ ✫✪ ✬✩ ✫✪ ✬✩ ✫✪ ✬✩ ▲ ▲ ▲ ▲ ▲ ▲ STORE SW DEP LAB south north east west south south north west east NE north west Figure 2: Transition between the locations 1 Non-determinism plays an important role in modeling domains such as a space shuttle in which much of the environment cannot be sensed remotely or cannot be tested at all until acted upon.