Satisfiability for Knowing How over Linear Plans is NP-complete

TL;DR

This paper proves that the satisfiability problem for a modal logic of knowing-how over linear plans is NP-complete, using a translation into modal logic S5 to improve previous complexity bounds.

Contribution

It establishes the NP-completeness of knowing-how satisfiability over linear plans, providing a new complexity result and a translation technique into modal logic S5.

Findings

Satisfiability of knowing-how formulas is NP-complete.

The proof uses a translation into modal logic S5.

Improves previous complexity bounds for the problem.

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.