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We show that the guarded-negation fragment (GNFO) is, in a precise sense, thesmallest extension of the guarded fragment (GFO) with Craig interpolation. Incontrast, we show that the smallest extension of the two-variable fragment(FO2), and of the forward fragment (FF) with Craig interpolation, is fullfirst-order logic. Similarly, we also show that all extensions of FO2 and ofthe fluted fragment (FL) with Craig interpolation are undecidable.

Craig Interpolation for Decidable First-Order Fragments