An Undecidability Proof for the Plan Existence Problem

📰 ArXiv cs.AI

Learn how the plan existence problem in modal logic is undecidable, even with simple preconditions, and why this matters for AI planning and decision-making

advanced Published 27 Apr 2026
Action Steps
  1. Read the paper to understand the plan existence problem and its formulation in modal logic
  2. Apply the concept of undecidability to AI planning and decision-making
  3. Analyze the implications of the proof for the design of autonomous systems
  4. Consider the limitations of AI reasoning in the context of modal logic
  5. Explore alternative approaches to addressing the plan existence problem
Who Needs to Know This

Researchers and engineers working on AI planning, decision-making, and modal logic will benefit from understanding the undecidability of the plan existence problem, as it has implications for the design of autonomous systems and the limits of AI reasoning

Key Insight

💡 The plan existence problem is undecidable, even with simple preconditions, which limits the ability of AI systems to reason about and plan for complex goals

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Undecidability of plan existence problem in modal logic has implications for AI planning & decision-making #AI #ModalLogic

Key Takeaways

Learn how the plan existence problem in modal logic is undecidable, even with simple preconditions, and why this matters for AI planning and decision-making

Full Article

Title: An Undecidability Proof for the Plan Existence Problem

Abstract:
arXiv:2604.22736v1 Announce Type: cross 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)deci
Read full paper → ← Back to Reads

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