Some Complexity and Correctness Results for Proof Planning

We prove that determining if a valid proof plan exists is undecidable in general, even if the meta-theory in which pre-and post-conditions are checked is itself decidable. On a more positive note, we prove that an iterative deepening proof planner is sound (only nds valid proof plans) and complete (if it terminates signaling failure or fails to terminate then no valid proof plan exists). We also show that a depth-rst proof planner is sound but not complete as there exist valid proof plans that it will not nd.