Satisfiability for Knowing How over Linear Plans is NP-complete
Logic in Computer Science
2026-05-20 v1
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.
Cite
@article{arxiv.2605.19819,
title = {Satisfiability for Knowing How over Linear Plans is NP-complete},
author = {Carlos Areces and Pablo Barceló and Valentin Cassano and Pablo F. Castro and Stéphane Demri and Raul Fervari},
journal= {arXiv preprint arXiv:2605.19819},
year = {2026}
}