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A Parametric Interpolation Framework for First-Order Theories

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Advances in Artificial Intelligence and Its Applications (MICAI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8265))

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Abstract

Craig interpolation is successfully used in both hardware and software model checking. Generating good interpolants, and hence automatically determining the quality of interpolants is however a very hard problem, requiring non-trivial reasoning in first-order theories. An important class of state-of-the-art interpolation algorithms is based on recursive procedures that generate interpolants from refutations of unsatisfiable conjunctions of formulas. We analyze this type of algorithms and develop a theoretical framework, called a parametric interpolation framework, for arbitrary first-order theories and inference systems. As interpolation-based verification approaches depend on the quality of interpolants, our method can be used to derive interpolants of different structure and strength, with or without quantifiers, from the same proof. We show that some well-known interpolation algorithms are instantiations of our framework.

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Author information

Authors and Affiliations

  1. Chalmers University of Technology, Sweden

    Laura Kovács

  2. USI, Switzerland

    Simone Fulvio Rollini & Natasha Sharygina

Authors
  1. Laura Kovács
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  2. Simone Fulvio Rollini
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  3. Natasha Sharygina
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Editor information

Editors and Affiliations

  1. Universidad Autónoma del Estado de Hidalgo, Ciudad Universitaria,, Carretera Pachuca–Tulancingo km 4.5, Hidalgo, Mexico

    FĂ©lix Castro

  2. Centro de Investigación en Computación, Instituto Politécnico Nacional, Av. Juan Dios Bátiz s/n, Col. Nueva Industrial Vallejo, 07738, Mexico City, Mexico

    Alexander Gelbukh

  3. Tecnológico de Monterrey, Campus Estado de México,, Carretera Lago de Guadalupe Km 3.5, Atizapán de Zaragoza,, CP 52926, Estado de México, Mexico

    Miguel González

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Kovács, L., Rollini, S.F., Sharygina, N. (2013). A Parametric Interpolation Framework for First-Order Theories. In: Castro, F., Gelbukh, A., González, M. (eds) Advances in Artificial Intelligence and Its Applications. MICAI 2013. Lecture Notes in Computer Science(), vol 8265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45114-0_3

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  • DOI: https://doi.org/10.1007/978-3-642-45114-0_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45113-3

  • Online ISBN: 978-3-642-45114-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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