A semantic approach to interpolation

Authors:
Andrei Popescu;Traian Florin erbnu;Grigore Rou
Affiliations:
Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States and Institute of Mathematics Simion Stoilow, Romanian Academy, Bucharest, Romania;Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States and Foundations of Computer Science, Faculty of Mathematics and Informatics, University ...;Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

Craig interpolation is investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for first-order logic. A few of these results non-trivially generalize known interpolation results; all the others are new. We also discuss some applications of our results to the theory of institutions and of algebraic specifications, and a Craig-Robinson version of these results.