---
title: "Finite-Valued Lukasiewicz Modal Logic Is PSPACE-Complete"
authors:
  - "Félix Bou"
  - "Marco Cerami"
  - "Francesc Esteva"
doi: "10.5591/978-1-57735-516-8/IJCAI11-136"
url: "https://ijcai.org/proceedings/2011/136"
pdf: "https://ijcai.org/proceedings/2011/0136.pdf"
venue: "Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence"
year: 2011
pages: "774-778"
track: ""
keywords:
---

# Finite-Valued Lukasiewicz Modal Logic Is PSPACE-Complete

Félix Bou, Marco Cerami, Francesc Esteva

*Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence*, pages 774-778. DOI: [10.5591/978-1-57735-516-8/IJCAI11-136](https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-136)

## Abstract

It is well-known that satisfiability (and hence validity) in the minimal classical modal logic is a PSPACE-complete problem. In this paper we consider the satisfiability and validity problems (here they are not dual, although mutually reducible) for the minimal modal logic over a finite Lukasiewicz chain, and show that they also are PSPACE-complete. This result is also true when adding either the Delta operator or truth constants in the language, i.e. in all these cases it is PSPACE-complete.