Giving Instructions in Linear Temporal Logic

Our aim is to develop a formal semantics for giving instructions to taskable agents, to investigate the complexity of decision problems relating to these semantics, and to explore the issues that these semantics raise. In the setting we consider, agents are given instructions in the form of Linear Temporal Logic (LTL) formulae; the intuitive interpretation of such an instruction is that the agent should act in such a way as to ensure the formula is satisfied. At the same time, agents are assumed to have inviolable and immutable background safety requirements, also specified as LTL formulae. Finally, the actions performed by an agent are assumed to have costs, and agents must act within a limited budget. For this setting, we present a range of interpretations of an instruction to achieve an LTL task Υ, intuitively ranging from “try to do this but only if you can do so with everything else remaining unchanged” up to “drop everything and get this done.” For each case we present a formal pre-/post-condition semantics, and investigate the computational issues that they raise.