Satisfiability for Knowing How over Linear Plans is NP-complete

2026-05-19

AI Summary

This study investigates the satisfiability problem for modal logic formulas expressing “knowing how” under a linear plan-based semantics. By translating these formulas into standard S5 modal logic and applying techniques from computational complexity theory, the paper establishes for the first time that the satisfiability problem is NP-complete. This result substantially improves upon previously known upper bounds and precisely characterizes the computational complexity of the logic’s satisfiability problem. Consequently, it provides a crucial theoretical foundation for the formal analysis of “knowing how” logics, advancing our understanding of their expressive power and algorithmic properties within epistemic reasoning frameworks.

Abstract

We study the satisfiability problem for a modal logic expressing knowing-how assertions, which captures an agent's ability to achieve a given goal under the standard semantics based on linear plans. Our main result shows that satisfiability of knowing-how formulas is NP-complete, improving previously known complexity bounds. The proof proceeds via a translation into modal logic S5, an instrumental tool for addressing a variety of problems in knowledge representation.

Problem

• satisfiability
• knowing-how
• modal logic
• linear plans
• NP-completeness

Innovation

• knowing-how
• satisfiability
• NP-complete
• modal logic
• linear plans