First-order progression for local-effect, normal, and acyclic actions is polynomial-sized and preserves decidable fragments such as two-variable logic.
Living without beth and craig: Definitions and interpolants in the guarded and two-variable fragments
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On the Size Complexity and Decidability of First-Order Progression
First-order progression for local-effect, normal, and acyclic actions is polynomial-sized and preserves decidable fragments such as two-variable logic.