Interpolation and Uniform Interpolation in Quantifier-Free Fragments of Combined First-Order Theories

Silvio Ghilardi and Alessandro Gianola
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Silvio Ghilardi: Department of Mathematics, Universitá degli Studi di Milano, 20133 Milan, Italy
Alessandro Gianola: Faculty of Computer Science, Free University of Bozen-Bolzano, 39100 Bolzano, Italy

Mathematics, 2022, vol. 10, issue 3, 1-22

Abstract: In this survey, we report our recent work concerning combination results for interpolation and uniform interpolation in the context of quantifier-free fragments of first-order theories. We stress model-theoretic and algebraic aspects connecting this topic with amalgamation, strong amalgamation, and model-completeness. We give sufficient (and, in relevant situations, also necessary) conditions for the transfer of the quantifier-free interpolation property to combined first-order theories; we also investigate the non-disjoint signature case under the assumption that the shared theory is universal Horn. For convex, strong-amalgamating, stably infinite theories over disjoint signatures, we also provide a modular transfer result for the existence of uniform interpolants. Model completions play a key role in the whole paper: They enter into transfer results in the non-disjoint signature case and also represent a semantic counterpart of uniform interpolants.

Keywords: interpolation; combined interpolation; uniform interpolation; satisfiability modulo theories (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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