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arXiv · 2310.08689

Craig Interpolation for Decidable First-Order Fragments

Balder ten Cate·Jesse Comer
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Abstract

We show that the guarded-negation fragment is, in a precise sense, the smallest extension of the guarded fragment with Craig interpolation. In contrast, we show that full first-order logic is the smallest extension of both the two-variable fragment and the forward fragment with Craig interpolation. Similarly, we also show that all extensions of the two-variable fragment and of the fluted fragment with Craig interpolation are undecidable.

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Balder ten Cate, Jesse Comer. 2023-10-12. Craig Interpolation for Decidable First-Order Fragments. https://doi.org/10.46298/lmcs-21(3:22)2025

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