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Ibero-American Conference on Artificial Intelligence

IBERAMIA 2002: Advances in Artificial Intelligence — IBERAMIA 2002 pp 161–171Cite as

Restricted Δ-Trees and Reduction Theorems in Multiple-Valued Logics

Part of the Lecture Notes in Computer Science book series (LNAI,volume 2527)

Abstract

In this paper we continue the theoretical study of the possible applications of the Δ-tree data structure for multiple-valued logics, specifically, to be applied to signed propositional formulas. The Δ-trees allow a compact representation for signed formulas as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfiability of the input formula. New and improved versions of reduction theorems for finite-valued propositional logics are introduced, and a satisfiability algorithm is provided which further generalise the TAS method [1],[5].

Research partially supported by Spanish DGI project BFM2000-1054-C02-02 and Junta de Andalucía project TIC-115.

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References

  1. G. Aguilera, I. P. de Guzmán, M. Ojeda-Aciego, and A. Valverde. Reductions for non-clausal theorem proving. Theoretical Computer Science, 266(1/2):81–112, 2001.

    CrossRef  MATH  MathSciNet  Google Scholar 

  2. S. Aguzzoli and A. Ciabattoni. Finiteness in infinite-valued Lukasiewicz logic. Journal of Logic, Language and Information, 9(1):5–29, 2000.

    CrossRef  MATH  MathSciNet  Google Scholar 

  3. C. Files, R. Drechsler, and M. Perkowski. Functional decomposition of MVL functions using multi-valued decision diagrams. In Proc. ISMVL’97, pages 7–32, 1997.

    Google Scholar 

  4. G. Gutiérrez, I. P. de Guzmán, J. Martínez, M. Ojeda-Aciego, and A. Valverde. Satisfiability testing for Boolean formulas using Δ-trees. Studia Logica, 72:33–60, 2002.

    CrossRef  Google Scholar 

  5. I. P. de Guzmán, M. Ojeda-Aciego, and A. Valverde. Reducing signed propositional formulas. Soft Computing, 2(4):157–166, 1999.

    Google Scholar 

  6. I. P. de Guzmán, M. Ojeda-Aciego, and A. Valverde. Restricted Δ-trees in multiple-valued logics. In AI-Methodologies, Systems, Applications. AIMSA’02. Lect. Notes in Computer Science 2443, 2002.

    Google Scholar 

  7. R. Hähnle. Uniform notation of tableaux rules for multiple-valued logics. In Proc. Intl Symp on Multiple-Valued Logic, pages 238–245. IEEE Press, 1991.

    Google Scholar 

  8. D. Mundici and N. Olivetti. Resolution and model building in the infinite-valued calculus of Lukasiewicz. Theoretical Computer Science, 200:335–366, 1998.

    CrossRef  MATH  MathSciNet  Google Scholar 

  9. N. V. Murray and E. Rosenthal. Improving tableau deductions in multiple-valued logics. In Proc. 21st Intl Symp on Multiple-Valued Logic, pages 230–237. IEEE Press, 1991.

    Google Scholar 

  10. D. Pearce, I. P. de Guzmán, and A. Valverde. Computing equilibrium models using signed formulas. In Proc. 1st Intl Conf on Computational Logic, CL’2000, Lect. Notes in Artificial Intelligence 1861, pages 688–702, 2000.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. Matemática Aplicada, Universidad de Málaga, Germany

    Inma P. de Guzmán, Manuel Ojeda-Aciego & Agustín Valverde

Authors
  1. Inma P. de Guzmán
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  2. Manuel Ojeda-Aciego
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  3. Agustín Valverde
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Editor information

Editors and Affiliations

  1. Telefónica Investigación y Desarrollo, Emilio Vargas 6, 28043, Madrid, Spain

    Francisco J. Garijo

  2. Dpto. Lenguajes y Sistemas Informáticos, Universidad de Sevilla, ETS Ingeniería Informática, 41012, Seville, Spain

    José C. Riquelme & Miguel Toro & 

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© 2002 Springer-Verlag Berlin Heidelberg

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de Guzmán, I.P., Ojeda-Aciego, M., Valverde, A. (2002). Restricted Δ-Trees and Reduction Theorems in Multiple-Valued Logics. In: Garijo, F.J., Riquelme, J.C., Toro, M. (eds) Advances in Artificial Intelligence — IBERAMIA 2002. IBERAMIA 2002. Lecture Notes in Computer Science(), vol 2527. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36131-6_17

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  • DOI: https://doi.org/10.1007/3-540-36131-6_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00131-7

  • Online ISBN: 978-3-540-36131-2

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