Skip to main content
SpringerLink
Log in

Efficient Unfolding of Fuzzy Connectives for Multi-adjoint Logic Programs

  • Chapter
  • First Online:
Interactions Between Computational Intelligence and Mathematics

Part of the book series: Studies in Computational Intelligence ((SCI,volume 758))

  • 399 Accesses

Abstract

During the last decade we have designed several tools for assisting the development of flexible software applications coded with a promising language in the fuzzy logic programming area. In the so-called multi-adjoint logic programming approach, a set of logic rules are assembled with a set of fuzzy connective definitions (whose truth functions are defined as functional rules) for manipulating truth degrees beyond the simpler case of {true,false}. Moreover, we have recently provided optimization techniques by reusing some variants of program transformation techniques based on unfolding which have been largely exploited in the pure functional -not fuzzy- setting for enhancing the behavior of such operators. In this paper we experimentally show the benefits of using the new c-unfolding transformation applied on fuzzy connectives and how to improve the efficiency of the proper unfolding process by reusing the very well-known concept of dependency graph. Moreover, we accompany our technique with cost analysis and discussions on practical aspects.

This work has been partially supported by the EU (FEDER), the State Research Agency (AEI) and the Spanish Ministerio de Economía y Competitividad under grant TIN2016-76843-C4-2-R (AEI/FEDER, UE).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    In essence, both languages share the same syntax, but they have a different computational behaviour since Curry  extends with extra logic features the pure functional dimension of Haskell.

References

  1. Almendros-Jiménez, J.M., Bofill, M., Luna Tedesqui, A., Moreno, G., Vázquez, C., Villaret, M.: Fuzzy xpath for the automatic search of fuzzy formulae models. In: Beierle, C., Dekhtyar A. (eds.) Scalable Uncertainty Management—9th International Conference, SUM 2015, Québec City, QC, Canada, September 16–18, 2015. Proceedings, volume 9310 of Lecture Notes in Computer Science, 385–398. Springer, 2015

    Google Scholar 

  2. Almendros-Jiménez, J.M., Luna, A., Moreno, G.: Fuzzy logic programming for implementing a flexible xpath-based query language. Electron. Notes Theor. Comput. Sci. 282, 3–18 (2012)

    Article  Google Scholar 

  3. Almendros-Jiménez, J.M., Luna, A., Moreno, G.: Fuzzy xpath through fuzzy logic programming. New Generation Computing 33(2), 173–209 (2015)

    Article  Google Scholar 

  4. Alpuente, M., Falaschi, M., Moreno, G., Vidal, G.: Rules + strategies for transforming lazy functional logic programs. Theoretical Comput. Sci. Elsevier 311(1–3), 479–525 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theor. Comput. Sci. 236(1–2), 133–178 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)

    Book  MATH  Google Scholar 

  7. Baldwin, J.F., Martin, T.P., Pilsworth, B.W.: Fril- Fuzzy and Evidential Reasoning in Artificial Intelligence. Wiley, New Yark (1995)

    Google Scholar 

  8. Burstall, R.M., Darlington, J.: A transformation system for developing recursive programs. J. ACM 24(1), 44–67 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  9. Guerrero, J.A., Martínez, M.S., Moreno, G., Vázquez, C.: Designing lattices of truth degrees for fuzzy logic programming environments. In: IEEE Symposium Series on Computational Intelligence, SSCI 2015, Cape Town, South Africa, December 7–10, 2015, pp. 995–1004 IEEE, 2015

    Google Scholar 

  10. Guerrero, J.A., Moreno, G.: Optimizing fuzzy logic programs by unfolding, aggregation and folding. Electron. Notes Theor. Comput. Sci. 219, 19–34 (2008)

    Article  MATH  Google Scholar 

  11. Hanus, M. (ed.): Curry: An integrated functional logic language (vers. 0.8.3). Available at http://www.curry-language.org, (2012)

  12. Huet, G., Lévy, J.J.: Computations in orthogonal rewriting systems, Part I + II. In: Lassez, J.L., Plotkin, G.D. (eds.) Computational logic—essays in honor of alan robinson, pp. 395–443. The MIT Press, Cambridge, MA (1992)

    Google Scholar 

  13. Hutton, Graham: Programming in Haskell. Cambridge University Press, Cambridge (2007)

    Book  MATH  Google Scholar 

  14. Ishizuka, M., Kanai, N.: Prolog-ELF Incorporating Fuzzy Logic. In Joshi, A.K. (eds.) Proceedings of the 9th International Joint Conference on Artificial Intelligence, IJCAI’85, 701–703. Morgan Kaufmann, 1985

    Google Scholar 

  15. Julián Iranzo, P., Moreno, G., Penabad, J., Vázquez, C.: A declarative semantics for a fuzzy logic language managing similarities and truth degrees. In: Alferes, J., Bertossi, L.E., Governatori, G., Fodor, P., Roman, D. (eds.) Rule Technologies. Research, Tools, and Applications—10th International Symposium, RuleML 2016, Stony Brook, NY, USA, July 6–9, 2016. Proceedings, volume 9718 of Lecture Notes in Computer Science, 68–82. Springer, 2016

    Google Scholar 

  16. Julián, P., Medina, J., Morcillo, P.J., Moreno, G., Ojeda-Aciego, M.: An unfolding-based preprocess for reinforcing thresholds in fuzzy tabulation. In: Proceedings of the 12th International Work-Conference on Artificial Neural Networks, IWANN’13, 647–655. Springer Verlag, LNCS 7902, Part I, 2013

    Google Scholar 

  17. Julián, P., Moreno, G., Penabad, J.: On fuzzy unfolding. a multi-adjoint approach. Fuzzy Sets Sys. 154, 16–33 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  18. Julián, P., Moreno, G., Penabad, J.: Operational/interpretive unfolding of multi-adjoint logic programs. J. Universal Comput. Sci. 12(11), 1679–1699 (2006)

    Google Scholar 

  19. Kifer, M., Subrahmanian, V.S.: Theory of generalized annotated logic programming and its applications. J. Logic Program. 12, 335–367 (1992)

    Article  MathSciNet  Google Scholar 

  20. Klop, J.W., Middeldorp, A.: Sequentiality in Orthogonal Term Rewriting Systems. J. Symbol. Comput. 161–195 (1991)

    Google Scholar 

  21. Lee, R.C.T.: Fuzzy logic and the resolution principle. J. ACM 19(1), 119–129 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  22. Lee, C., Jones, N., Ben-Amram, A.: The size-change principle for program termination. SIGPLAN Not. 36(3), 81–92 (2001)

    Article  MATH  Google Scholar 

  23. Li, D., Liu, D.: A fuzzy Prolog database system. Wiley, New Yark (1990)

    Google Scholar 

  24. Lloyd, J.W.: Foundations of Logic Programming. Springer-Verlag, Berlin (1987)

    Book  MATH  Google Scholar 

  25. Medina, J., Ojeda-Aciego, M., Vojtáš, P.: Multi-adjoint logic programming with continuous semantics. In: Proc of Logic Programming and Non-Monotonic Reasoning, LPNMR’01, vol. 2173, pp. 351–364. Springer-Verlag, LNAI, (2001)

    Google Scholar 

  26. Medina, J., Ojeda-Aciego, M., Vojtáš P.: A procedural semantics for multi-adjoint logic programing. In: Progress in Artificial Intelligence, EPIA’01, vol. 2258(1), pp. 290–297 Springer-Verlag, LNAI, (2001)

    Google Scholar 

  27. Medina, J., Ojeda-Aciego, M., Vojtáš, P.: Similarity-based Unification: a multi-adjoint approach. Fuzzy Sets Sys. 146, 43–62 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  28. Morcillo, P.J., Moreno, G., Penabad, J., Vázquez, C.: Fuzzy Computed Answers Collecting Proof Information. In: Cabestany, J., et al. (eds.) Advances in Computational Intelligence—Proceedings of the 11th International Work-Conference on Artificial Neural Networks, IWANN 2011, 445–452. Springer Verlag, LNCS 6692, 2011

    Google Scholar 

  29. Morcillo, P.J., Moreno, G.: Improving multi-adjoint logic programs by unfolding fuzzy connective definitions. In: Proceedings of the 13th International Work-Conference on Artificial Neural Networks, IWANN 2015 Mallorca, Spain, June 10–12, pp. 511–524. Springer Verlag, LNCS 9094, Part I, 2015

    Google Scholar 

  30. Morcillo, P.J., Moreno, G.: On cost estimations for executing fuzzy logic programs. In Arabnia, H.R. et al. (ed.) Proceedings of the 11th International Conference on Artificial Intelligence, ICAI 2009, July 13–16, 2009, Las Vegas (Nevada), USA

    Google Scholar 

  31. Morcillo, P.J., Moreno, G. Penabad, J., Vázquez, C.: A Practical Management of Fuzzy Truth Degrees using FLOPER. In: Dean, M., et al. (eds.) Proceedings of 4nd Intl Symposium on Rule Interchange and Applications, RuleML’10. Washington, USA, October 21–23, 20–34. Springer Verlag, LNCS 6403, 2010

    Google Scholar 

  32. Morcillo, P.J. Moreno, G.: Modeling interpretive steps in fuzzy logic computations. In: Di Gesù V. et al. (eds) Proceedings of the 8th International Workshop on Fuzzy Logic and Applications, WILF 2009. Palermo, Italy, June 9-12, 44–51. Springer Verlag, LNAI 5571, 2009

    Google Scholar 

  33. Moreno, G., Penabad, J., Vidal. G.: Tuning fuzzy logic programs with symbolic execution. CoRR, abs/1608.04688, 2016

    Google Scholar 

  34. Moreno, G.: Building a fuzzy transformation system. In: Wiedermann, J. et al. (eds.) Proceedings of the 32nd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM’2006. Merin, Czech Republic, January 21–27, 409–418. Springer Verlag, LNCS 3831, 2006

    Google Scholar 

  35. Moreno, Ginés: A narrowing-based instantiation rule for rewriting-based fold/unfold transformations. Electr. Notes Theor. Comput. Sci. 86(3), 144–167 (2003)

    Article  MATH  Google Scholar 

  36. Moreno, G., Vázquez, C.: Fuzzy logic programming in action with floper. J. Software Eng. Appl. 7, 273–298 (2014)

    Article  Google Scholar 

  37. Rodríguez-Artalejo, M., Romero-Díaz, C.: Quantitative logic programming revisited. In: Proceedings of 9th Functional and Logic Programming Symposium, FLOPS’08, 272–288. LNCS 4989, Springer Verlag, 2008

    Google Scholar 

  38. Straccia, U.: Managing uncertainty and vagueness in description logics, logic programs and description logic programs. In: Reasoning Web, 4th International Summer School, Tutorial Lectures, number 5224 in Lecture Notes in Computer Science, 54–103. Springer Verlag, 2008

    Google Scholar 

  39. Tamaki, H., Sato, T.: Unfold/Fold Transformations of Logic Programs. In: Tärnlund, S. (ed.) Proceedings of Second International Conference on Logic Programming, 127–139, 1984

    Google Scholar 

  40. Vázquez, C., Moreno, G.. Tomás, L., Tordsson, J.: A cloud scheduler assisted by a fuzzy affinity-aware engine. In: Yazici, A., Pal, N.R., Kaymak, U., Martin, T., Ishibuchi, H., Lin, C.-T., Sousa, J.M.C., Tütmez, B. (eds.) 2015 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2015, Istanbul, Turkey, August 2–5, 2015, 1–8. IEEE, 2015

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department Computing System, University of Castilla-La Mancha, 02071, Albacete, Spain

    Pedro J. Morcillo & Ginés Moreno

Authors
  1. Pedro J. Morcillo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ginés Moreno
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pedro J. Morcillo .

Editor information

Editors and Affiliations

  1. Faculty of Engineering Sciences, Széchenyi István University, Gyõr, Hungary

    László T. Kóczy

  2. Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cádiz, Puerto Real, Cádiz, Spain

    Jesús Medina

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Morcillo, P.J., Moreno, G. (2018). Efficient Unfolding of Fuzzy Connectives for Multi-adjoint Logic Programs. In: Kóczy, L., Medina, J. (eds) Interactions Between Computational Intelligence and Mathematics. Studies in Computational Intelligence, vol 758. Springer, Cham. https://doi.org/10.1007/978-3-319-74681-4_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-74681-4_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-74680-7

  • Online ISBN: 978-3-319-74681-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation