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.
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[1] http://www.iiia.csic.es/en/individual/felix-bou
[2] http://www.iiia.csic.es/en/individual/marco-cerami
[3] http://www.iiia.csic.es/en/individual/francesc-esteva
[4] http://www.iiia.csic.es/en/publications/export/tagged/4308
[5] http://www.iiia.csic.es/en/publications/export/xml/4308
[6] http://www.iiia.csic.es/en/publications/export/bib/4308
[7] http://www.iiia.csic.es/en/project/arinf
[8] http://www.iiia.csic.es/en/project/at
[9] http://www.iiia.csic.es/en/project/locomotion-0
[10] http://www.iiia.csic.es/en/project/sgr2009
[11] http://www.iiia.csic.es/en/project/tassat