One-variable, guarded, and two-variable-with-counting monodic fragments of first-order modal logics K_n and S5_n are decidable despite non-rigid constants, definite descriptions, and counting.
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Decidability in First-Order Modal Logic with Non-Rigid Constants and Definite Descriptions
One-variable, guarded, and two-variable-with-counting monodic fragments of first-order modal logics K_n and S5_n are decidable despite non-rigid constants, definite descriptions, and counting.