Conservative Extensions in Guarded and Two-Variable Fragments
Abstract
We investigate the decidability and computational complexity of (deductive) conservative extensions in fragments of first-order logic (FO), with a focus on the two-variable fragment FO2 and the guarded fragment GF. We prove that conservative extensions are undecidable in any FO fragment that contains FO2 or GF (even the three-variable fragment thereof), and that they are decidable and 2-complete in the intersection GF2 of FO2 and GF.
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