An Undecidability Proof for the Plan Existence Problem
TLDR
This paper proves the plan existence problem, even under simplified conditions, is undecidable, a previously unknown result.
Key contributions
- Proves the plan existence problem, concerning reaching a goal via epistemic actions, is undecidable.
- Demonstrates undecidability even when action preconditions have modal depth at most 1.
- Establishes this result even in the absence of any action postconditions.
- Resolves a long-standing open question about the problem's decidability.
Why it matters
This paper provides a fundamental theoretical result by proving the undecidability of the plan existence problem. This finding has significant implications for the design and limitations of automated planning systems, especially those dealing with knowledge and belief. It closes a previously open question in modal logic and AI planning.
Original Abstract
The plan existence problem asks, given a goal in the form of a formula in modal logic, an initial epistemic state (a pointed Kripke model), and a set of epistemic actions, whether there exists a sequence of actions that can be applied to reach the goal. We prove that even in the case where the preconditions of the epistemic actions have modal depth at most 1, and there are no postconditions, the plan existence problem is undecidable. The (un)decidability of this problem was previously unknown.
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