Modal Logic and the Two-Variable Fragment

Authors:
Carsten Lutz;Ulrike Sattler;Frank Wolter
Affiliations:
-;-;-
Venue:
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Year:
2001

Citing 11
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Abstract

We introduce a modal language L which is obtained from standard modal logic by adding the difference operator and modal operators interpreted by boolean combinations and the converse of accessibility relations. It is proved that L has the same expressive power as the two-variable fragment FO2 of first-order logic but speaks less succinctly about relational structures: if the number of relations is bounded, then L- satisfiability is EXPTIME-complete but FO2 satisfiability is NEXPTIME-complete. We indicate that the relation between L and FO2 provides a general framework for comparing modal and temporal languages with first-order languages.