SpringerLink
Log in

Hypergraphs in Logic Programming

  • Conference paper
  • First Online:
Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14294))

Abstract

Heterogeneous data is a significant topic in today’s context, necessitating the development of AI tools. Logic programming is a powerful approach for extracting information from datasets, enabling the interpretation of natural language as logical rules.

This paper introduces a novel representation of logic normal programs, which include negated variables, using labeled hypergraphs. This representation provides a comprehensive characterization of the program, capturing all available information and relationships among variables in a specific hypergraph. Such characterization is highly advantageous, particularly for computing program consequences and models through hypergraph theory.

Partially supported by the 2014–2020 ERDF Operational Programme in collaboration with the State Research Agency (AEI) in project PID2019-108991GB-I00, with the Ecological and Digital Transition Projects 2021 of the Ministry of Science and Innovation in project TED2021-129748B-I00, and with the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia in project FEDER-UCA18-108612, and by the European Cooperation in Science & Technology (COST) Action CA1712.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Berge, C.: Graphs and Hypergraphs. Elsevier Science Ltd., Amsterdam (1985)

    MATH  Google Scholar 

  2. Cornejo, M.E., Lobo, D., Medina, J.: Characterizing fuzzy y-models in multi-adjoint normal logic programming. In: Medina, J., Ojeda-Aciego, M., Verdegay, J.L., Perfilieva, I., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 2018. CCIS, vol. 855, pp. 541–552. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91479-4_45

    Chapter  MATH  Google Scholar 

  3. Cornejo, M.E., Lobo, D., Medina, J.: Syntax and semantics of multi-adjoint normal logic programming. Fuzzy Sets Syst. 345, 41–62 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cornejo, M.E., Lobo, D., Medina, J.: Extended multi-adjoint logic programming. Fuzzy Sets Syst. 388, 124–145 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cornejo, M.E., Lobo, D., Medina, J.: Relating multi-adjoint normal logic programs to core fuzzy answer set programs from a semantical approach. Mathematics 8(6), 1–18 (2020). Paper 881

    Article  Google Scholar 

  6. Damásio, C., Medina, J., Ojeda-Aciego, M.: Termination of logic programs with imperfect information: applications and query procedure. J. Appl. Log. 5, 435–458 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Díaz-Moreno, J.C., Medina, J., Portillo, J.R.: Towards the use of hypergraphs in multi-adjoint logic programming. Stud. Comput. Intell. 796, 53–59 (2019)

    Article  MATH  Google Scholar 

  8. Díaz-Moreno, J.C., Medina, J., Portillo, J.R.: Fuzzy logic programs as hypergraphs. Termination results. Fuzzy Sets Syst. 445, 22–42 (2022). Logic and Databases

    Article  MathSciNet  MATH  Google Scholar 

  9. Emden, M.V., Kowalski, R.: The semantics of predicate logic as a programming language. J. ACM 23(4), 733–742 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  10. Gallo, G., Longo, G., Pallottino, S., Nguyen, S.: Directed hypergraphs and applications. Discrete Appl. Math. 42(2–3), 177–201 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  11. Halpin, H., McNeill, F.: Discovering meaning on the go in large heterogenous data. Artif. Intell. Rev. 40, 107–126 (2013)

    Article  Google Scholar 

  12. Julián-Iranzo, P., Moreno, G., Riaza, J.A.: Some properties of substitutions in the framework of similarity relations. Fuzzy Sets Syst. 465, 108510 (2023)

    Article  MathSciNet  Google Scholar 

  13. Julián-Iranzo, P., Sáenz-Pérez, F.: Bousi\(\sim \)prolog: design and implementation of a proximity-based fuzzy logic programming language. Expert Syst. Appl. 213, 118858 (2023)

    Article  Google Scholar 

  14. Kulagin, K., Salikhov, M., Burnashev, R.: Designing an educational intelligent system with natural language processing based on fuzzy logic. In: 2023 International Russian Smart Industry Conference (SmartIndustryCon), pp. 690–694 (2023)

    Google Scholar 

  15. Madrid, N., Ojeda-Aciego, M.: On the existence and unicity of stable models in normal residuated logic programs. Int. J. Comput. Math. 89(3), 310–324 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Medina, J., Ojeda-Aciego, M., Vojtaš, P.: Multi-adjoint logic programming with continous semantics. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 351–364. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45402-0_26

    Chapter  MATH  Google Scholar 

  17. Medina, J., Torné-Zambrano, J.A.: Immediate consequences operator on generalized quantifiers. Fuzzy Sets Syst. 456, 72–91 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  18. Mooney, R.J.: Inductive logic programming for natural language processing. In: Muggleton, S. (ed.) ILP 1996. LNCS, vol. 1314, pp. 1–22. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-63494-0_45

    Chapter  Google Scholar 

  19. Nakamura, K., Ando, T.: A taboo-not in open world assumption for a natural language based logic programming. In: 2022 IEEE International Conference on Big Data (Big Data), pp. 5140–5144 (2022)

    Google Scholar 

  20. Regaieg, R., Koubàa, M., Osei-Opoku, E., Aguili, T.: A two objective linear programming model for VM placement in heterogenous data centers. In: Boudriga, N., Alouini, M.-S., Rekhis, S., Sabir, E., Pollin, S. (eds.) UNet 2018. LNCS, vol. 11277, pp. 167–178. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-02849-7_15

    Chapter  Google Scholar 

  21. Ren, M., Zhang, Z., Zhang, J., Mora, L.: Understanding the use of heterogenous data in tackling urban flooding: an integrative literature review. Water 14(14), 2160 (2022)

    Article  Google Scholar 

  22. Salazar, E., Gupta, G.: Proof-theoretic foundations of normal logic programs. In: Lopez-Garcia, P., Gallagher, J.P., Giacobazzi, R. (eds.) Analysis, Verification and Transformation for Declarative Programming and Intelligent Systems. Lecture Notes in Computer Science, vol. 13160, pp. 233–252. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-31476-6_13

    Chapter  Google Scholar 

  23. Scherr, S.A., Hupp, S., Elberzhager, F.: Establishing continuous app improvement by considering heterogenous data sources. Int. J. Interact. Mob. Technol. (iJIM) 15(10), 66–86 (2021)

    Article  Google Scholar 

  24. Wachtel, A., Fuchß, D., Przybylla, M., Tichy, W.F.: Natural language data queries on multiple heterogenous data sources. In: Malizia, A., Valtolina, S., Morch, A., Serrano, A., Stratton, A. (eds.) IS-EUD 2019. LNCS, vol. 11553, pp. 174–182. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-24781-2_13

    Chapter  Google Scholar 

  25. Wang, Y., Eiter, T., Zhang, Y., Lin, F.: Witnesses for answer sets of logic programs. ACM Trans. Comput. Logic 24(2), 1–46 (2023)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Cádiz, Cádiz, Spain

    Juan Carlos Díaz-Moreno & Jesús Medina

  2. Departamento de Matemática Aplicada 1, Universidad de Sevilla, Sevilla, Spain

    José R. Portillo

  3. Instituto Universitario de Investigación de Matemáticas de la Universidad de Sevilla (IMUS), Sevilla, Spain

    José R. Portillo

Authors
  1. Juan Carlos Díaz-Moreno
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jesús Medina
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. José R. Portillo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jesús Medina .

Editor information

Editors and Affiliations

  1. CRIL CNRS University Artois, Lens Cedex, France

    Zied Bouraoui

  2. CRIL CNRS University Artois, Lens Cedex, France

    Srdjan Vesic

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Díaz-Moreno, J.C., Medina, J., Portillo, J.R. (2024). Hypergraphs in Logic Programming. In: Bouraoui, Z., Vesic, S. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2023. Lecture Notes in Computer Science(), vol 14294. Springer, Cham. https://doi.org/10.1007/978-3-031-45608-4_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-45608-4_33

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-45607-7

  • Online ISBN: 978-3-031-45608-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation