## Edith Hemaspaandra

Department of Computer Science

Rochester Institute of Technology

102 Lomb Memorial Drive

Rochester, NY 14623-5608

eh@cs.rit.edu

www.cs.rit.edu/~eh

### Abstract

Motivated by description logics, we investigate what happens to the
complexity of modal satisfiability problems if we only allow formulas built
from literals, conjunction, diamonds and boxes.
Previously, the only known result was that the complexity of the satisfiabili
ty
problem for **K** dropped from PSPACE-complete to coNP-complete
(Schmidt-Schauss and Smolka 1991), (Donini et al. 1992).
In this paper we show that not all logics behave like **K**.
In particular, we show that the complexity of the satisfiability problem with
respect to frames in which each world has at least one successor drops from
PSPACE-complete to P, but that in contrast the satisfiability problem with
respect to the class of frames in which each world has at most two successors
remains PSPACE-complete.
As a corollary of the latter result, we also solve the one missing case from
the complexity classification of description logics in (Donini et al. 1997).

Dvi-file

PS-File

PDF-File

Bibtex Entry