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The Inverse Method for Many-Valued Logics

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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

We define an automatic proof procedure for finitely many-valued logics given by truth tables. The proof procedure is based on the inverse method. To define this procedure, we introduce so-called introduction-based sequent calculi. By studying proof-theoretic properties of these calculi we derive efficient validity- and satisfiability-checking procedures based on the inverse method. We also show how to translate the validity problem for a formula to unsatisfiability checking of a set of propositional clauses.

We acknowledge funding from the Austrian FWF grant S11410-N23 and the Austrian WWTF grant ICT C-050.

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Author information

Authors and Affiliations

  1. Chalmers University of Technology, Sweden

    Laura Kovács

  2. Irkutsk State University, Russia

    Andrei Mantsivoda

  3. The University of Manchester, UK

    Andrei Voronkov

Authors
  1. Laura Kovács
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  2. Andrei Mantsivoda
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  3. Andrei Voronkov
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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., Mantsivoda, A., Voronkov, A. (2013). The Inverse Method for Many-Valued Logics. 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_2

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  • DOI: https://doi.org/10.1007/978-3-642-45114-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45113-3

  • Online ISBN: 978-3-642-45114-0

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