English

On the Complexity of Elementary Modal Logics

Computational Complexity 2008-02-14 v1 Logic in Computer Science

Abstract

Modal logics are widely used in computer science. The complexity of modal satisfiability problems has been investigated since the 1970s, usually proving results on a case-by-case basis. We prove a very general classification for a wide class of relevant logics: Many important subclasses of modal logics can be obtained by restricting the allowed models with first-order Horn formulas. We show that the satisfiability problem for each of these logics is either NP-complete or PSPACE-hard, and exhibit a simple classification criterion. Further, we prove matching PSPACE upper bounds for many of the PSPACE-hard logics.

Keywords

Cite

@article{arxiv.0802.1884,
  title  = {On the Complexity of Elementary Modal Logics},
  author = {Edith Hemaspaandra and Henning Schnoor},
  journal= {arXiv preprint arXiv:0802.1884},
  year   = {2008}
}

Comments

Full version of STACS 2008 paper

R2 v1 2026-06-21T10:12:21.431Z