On the existence and unicity of stable models in normal residuated logic programs

uncategorised

Authors

Nicolás Madrid

Manuel Ojeda-Aciego

Published

1 January 2012

Publication details

Int. J. Comput. Math. vol. 89 (3), pages 310–324.

Links

Abstract

We introduce a sufficient condition which guarantees the existence of stable models for a normal residuated logic program interpreted on the truth-space [0, 1] n . Specifically, the continuity of the connectives involved in the program ensures the existence of stable models. Then, we study conditions which guarantee the uniqueness of stable models in the particular case of the product t-norm, its residuated implication and the standard negation.

Citation

Please, cite this work as:

[MO12] N. Madrid and M. Ojeda-Aciego. “On the existence and unicity of stable models in normal residuated logic programs”. In: Int. J. Comput. Math. 89.3 (2012), pp. 310-324. DOI: 10.1080/00207160.2011.580842. URL: https://doi.org/10.1080/00207160.2011.580842.

BibTeX

@Article{Madrid2012,
     author = {Nicol{’a}s Madrid and Manuel Ojeda-Aciego},
     journal = {Int. J. Comput. Math.},
     title = {On the existence and unicity of stable models in normal residuated logic programs},
     year = {2012},
     number = {3},
     pages = {310–324},
     volume = {89},
     bibsource = {dblp computer science bibliography, https://dblp.org},
     biburl = {https://dblp.org/rec/journals/ijcm/MadridO12.bib},
     doi = {10.1080/00207160.2011.580842},
     timestamp = {Mon, 03 Jan 2022 00:00:00 +0100},
     url = {https://doi.org/10.1080/00207160.2011.580842},
}

Bibliometric data

The following data has been extracted from resources such as OpenAlex, Dimensions, PlumX or Altmetric.

Citations
CrossRef - Citation Indexes: 4
Scopus - Citation Indexes: 21

Captures
Mendeley - Readers: 5

Cites

The following graph plots the number of cites received by this work from its publication, on a yearly basis.

Papers citing this work

The following is a non-exhaustive list of papers that cite this work:

[1] M. Blondeel, S. Schockaert, D. Vermeir, et al. “Complexity of fuzzy answer set programming under Łukasiewicz semantics”. In: International Journal of Approximate Reasoning 55.9 (Dec. 2014), p. 1971–2003. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2013.10.011. URL: http://dx.doi.org/10.1016/j.ijar.2013.10.011.

[2] M. E. Cornejo, D. Lobo, and J. Medina. “Characterizing Fuzzy y-Models in Multi-adjoint Normal Logic Programming”. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. Springer International Publishing, 2018, p. 541–552. ISBN: 9783319914794. DOI: 10.1007/978-3-319-91479-4_45. URL: http://dx.doi.org/10.1007/978-3-319-91479-4_45.

[3] M. E. Cornejo, D. Lobo, and J. Medina. “Extended multi-adjoint logic programming”. In: Fuzzy Sets and Systems 388 (Jun. 2020), p. 124–145. ISSN: 0165-0114. DOI: 10.1016/j.fss.2019.03.016. URL: http://dx.doi.org/10.1016/j.fss.2019.03.016.

[4] M. E. Cornejo, D. Lobo, and J. Medina. “Measuring the Incoherent Information in Multi-adjoint Normal Logic Programs”. In: Advances in Fuzzy Logic and Technology 2017. Springer International Publishing, Sep. 2017, p. 521–533. ISBN: 9783319668307. DOI: 10.1007/978-3-319-66830-7_47. URL: http://dx.doi.org/10.1007/978-3-319-66830-7_47.

[5] M. E. Cornejo, D. Lobo, and J. Medina. “Relating Multi-Adjoint Normal Logic Programs to Core Fuzzy Answer Set Programs from a Semantical Approach”. In: Mathematics 8.6 (Jun. 2020), p. 881. ISSN: 2227-7390. DOI: 10.3390/math8060881. URL: http://dx.doi.org/10.3390/math8060881.

[6] M. E. Cornejo, D. Lobo, and J. Medina. “Stratified extended multi-adjoint logic programming”. In: Fuzzy Sets and Systems 492 (Sep. 2024), p. 109064. ISSN: 0165-0114. DOI: 10.1016/j.fss.2024.109064. URL: http://dx.doi.org/10.1016/j.fss.2024.109064.

[7] M. E. Cornejo, D. Lobo, and J. Medina. “Syntax and semantics of multi-adjoint normal logic programming”. In: Fuzzy Sets and Systems 345 (Aug. 2018), p. 41–62. ISSN: 0165-0114. DOI: 10.1016/j.fss.2017.12.009. URL: http://dx.doi.org/10.1016/j.fss.2017.12.009.

[8] M. E. Cornejo, J. Medina, and E. Ramírez-Poussa. “Adjoint negations, more than residuated negations”. In: Information Sciences 345 (Jun. 2016), p. 355–371. ISSN: 0020-0255. DOI: 10.1016/j.ins.2016.01.038. URL: http://dx.doi.org/10.1016/j.ins.2016.01.038.

[9] J. C. Díaz-Moreno, J. Medina, and J. R. Portillo. “Fuzzy logic programs as hypergraphs. Termination results”. In: Fuzzy Sets and Systems 445 (Sep. 2022), p. 22–42. ISSN: 0165-0114. DOI: 10.1016/j.fss.2022.02.001. URL: http://dx.doi.org/10.1016/j.fss.2022.02.001.

[10] J. C. Díaz-Moreno, J. Medina, and J. R. Portillo. “Hypergraphs in Logic Programming”. In: Symbolic and Quantitative Approaches to Reasoning with Uncertainty. Springer Nature Switzerland, Nov. 2023, p. 442–452. ISBN: 9783031456084. DOI: 10.1007/978-3-031-45608-4_33. URL: http://dx.doi.org/10.1007/978-3-031-45608-4_33.

[11] J. JANSSEN, D. VERMEIR, S. SCHOCKAERT, et al. “Reducing fuzzy answer set programming to model finding in fuzzy logics”. In: Theory and Practice of Logic Programming 12.6 (Jun. 2011), p. 811–842. ISSN: 1475-3081. DOI: 10.1017/s1471068411000093. URL: http://dx.doi.org/10.1017/s1471068411000093.

[12] V. H. Le. “Extending Fuzzy Linguistic Logic Programming with Negation †”. In: Mathematics 10.17 (Aug. 2022), p. 3105. ISSN: 2227-7390. DOI: 10.3390/math10173105. URL: http://dx.doi.org/10.3390/math10173105.

[13] V. H. Le. “The Stable Model Semantics of Normal Fuzzy Linguistic Logic Programs”. In: Computational Collective Intelligence. Springer International Publishing, 2019, p. 53–65. ISBN: 9783030283773. DOI: 10.1007/978-3-030-28377-3_5. URL: http://dx.doi.org/10.1007/978-3-030-28377-3_5.

[14] D. Lobo, M. E. Cornejo Piñero, and J. Medina. “Abductive reasoning in normal residuated logic programming via bipolar max-product fuzzy relation equations”. In: Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (EUSFLAT 2019). eusflat-19. Atlantis Press, 2019. DOI: 10.2991/eusflat-19.2019.81. URL: http://dx.doi.org/10.2991/eusflat-19.2019.81.

[15] N. Madrid. “A sufficient condition to guarantee the existence of fuzzy stable models on residuated logic programming with constrains”. In: 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, Jul. 2017, p. 1–6. DOI: 10.1109/fuzz-ieee.2017.8015741. URL: http://dx.doi.org/10.1109/fuzz-ieee.2017.8015741.

[16] N. Madrid, J. Medina, and E. Ramírez-Poussa. “Rough sets based on Galois connections”. In: International Journal of Applied Mathematics and Computer Science 30.2 (2020). ISSN: 2083-8492. DOI: 10.34768/amcs-2020-0023. URL: http://dx.doi.org/10.34768/amcs-2020-0023.

[17] N. Madrid and M. Ojeda-Aciego. “Modelling fuzzy partitions with fuzzy answer sets”. In: 2017 IEEE Symposium Series on Computational Intelligence (SSCI). IEEE, Nov. 2017, p. 1–8. DOI: 10.1109/ssci.2017.8285308. URL: http://dx.doi.org/10.1109/ssci.2017.8285308.

[18] N. Madrid and M. Ojeda-Aciego. “Multi-adjoint lattices from adjoint triples with involutive negation”. In: Fuzzy Sets and Systems 405 (Feb. 2021), p. 88–105. ISSN: 0165-0114. DOI: 10.1016/j.fss.2019.12.004. URL: http://dx.doi.org/10.1016/j.fss.2019.12.004.

[19] N. Madrid and M. Ojeda-Aciego. “On the use of fuzzy stable models for inconsistent classical logic programs”. In: 2011 IEEE Symposium on Foundations of Computational Intelligence (FOCI). IEEE, Apr. 2011, p. 115–121. DOI: 10.1109/foci.2011.5949476. URL: http://dx.doi.org/10.1109/foci.2011.5949476.

[20] N. Madrid and M. Ojeda-Aciego. “The f-index of inclusion as optimal adjoint pair for fuzzy modus ponens”. In: Fuzzy Sets and Systems 466 (Aug. 2023), p. 108474. ISSN: 0165-0114. DOI: 10.1016/j.fss.2023.01.009. URL: http://dx.doi.org/10.1016/j.fss.2023.01.009.

[21] N. Madrid and M. Ojeda‐Aciego. “A measure of consistency for fuzzy logic theories”. In: Mathematical Methods in the Applied Sciences 46.15 (May. 2021), p. 15982–15995. ISSN: 1099-1476. DOI: 10.1002/mma.7470. URL: http://dx.doi.org/10.1002/mma.7470.

[22] C. Marco, C. Jorge, and L. João. “On the Efficient Implementation of Social Abstract Argumentation”. In: ECAI 2014. IOS Press, 2014. DOI: 10.3233/978-1-61499-419-0-225. URL: http://dx.doi.org/10.3233/978-1-61499-419-0-225.

[23] J. Vigo-Aguiar, J. C. Reboredo, and H. R. Calle. “Topics of contemporary computational mathematics”. In: International Journal of Computer Mathematics 89.3 (Feb. 2012), p. 265–267. ISSN: 1029-0265. DOI: 10.1080/00207160.2012.649131. URL: http://dx.doi.org/10.1080/00207160.2012.649131.