English

How Easy it is to Know How: An Upper Bound for the Satisfiability Problem

Logic in Computer Science 2023-10-02 v1

Abstract

We investigate the complexity of the satisfiability problem for a modal logic expressing `knowing how' assertions, related to an agent's abilities to achieve a certain goal. We take one of the most standard semantics for this kind of logics based on linear plans. Our main result is a proof that checking satisfiability of a `knowing how' formula can be done in Σ2P\Sigma_2^P. The algorithm we present relies on eliminating nested modalities in a formula, and then performing multiple calls to a satisfiability checking oracle for propositional logic.

Keywords

Cite

@article{arxiv.2309.17094,
  title  = {How Easy it is to Know How: An Upper Bound for the Satisfiability Problem},
  author = {Carlos Areces and Valentin Cassano and Raul Fervari and Pablo Castro and Andres Saravia},
  journal= {arXiv preprint arXiv:2309.17094},
  year   = {2023}
}
R2 v1 2026-06-28T12:35:53.705Z