Modal Logic and the Two-Variable Fragment
نویسندگان
چکیده
We introduce a modal language L which is obtained from standard modal logic by adding the Boolean operators on accessibility relations, the identity relation, and the converse of relations. It is proved that L has the same expressive power as the two-variable fragment FO of first-order logic, but speaks less succinctly about relational structures: if the number of relations is bounded, then L-satisfiability is ExpTimecomplete but FO satisfiability is NExpTime-complete. We indicate that the relation between L and FO provides a general framework for comparing modal and temporal languages with first-order languages.
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