Conservative Extensions in Guarded and Two-Variable Fragments
Jean Christoph Jung, Carsten Lutz, Mauricio Martel, Thomas Schneider, Frank Wolter · arXiv (Cornell University) · 2017
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 FO$^2$ and the guarded fragment GF. We prove that conservative extensions are undecidable in any FO fragment that contains FO$^2$ or GF (even the three-variable fragment thereof), and that they are decidable and 2\ExpTime-complete in the intersection GF$^2$ of FO$^2$ and GF.