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 FO 2 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 FO 2 satisfiability is NE xp Time-complete. We indicate that the relation between L and FO 2 provides a general framework for comparing modal and temporal languages with first-order languages.
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Lutz, C., Sattler, U., Wolter, F. (2001). Modal Logic and the Two-Variable Fragment. In: Fribourg, L. (eds) Computer Science Logic. CSL 2001. Lecture Notes in Computer Science, vol 2142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44802-0_18
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DOI: https://doi.org/10.1007/3-540-44802-0_18
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