Situation Calculus Temporally Lifted Abstractions for Generalized Planning

We present a new formal framework for generalized planning (GP) based on the situation calculus extended with LTL constraints. The GP problem is specified by a first-order basic action theory whose models are the problem instances. This low-level theory is then abstracted into a high-level propositional nondeterministic basic action theory with a single model. A refinement mapping relates the two theories. LTL formulas are used to specify the temporally extended goals as well as assumed trace constraints. If all LTL trace constraints hold at the low level and the high-level model can simulate all the low-level models with respect to the mapping, we say that we have a temporally lifted abstraction. We prove that if we have such an abstraction and the agent has a strategy to achieve a LTL goal under some trace constraints at the abstract level, then there exists a refinement of the strategy to achieve the refinement of the goal at the concrete level. We use LTL synthesis to generate the strategy at the abstract level. We illustrate our approach by synthesizing a program that solves a data structure manipulation problem.