On the measure of incoherence in extended residuated logic programs

 

Abstract

In this paper we continue analyzing the introduction of negation into the framework of residuated logic programming [18], [19]; specifically, we focus on extended programs, in which strong negation is introduced. The classical approach to extended logic programs consists in considering negated literals as new, independent, ones and, then apply the usual monotonic approach (based on the fix-point semantics and the T _P operator); if the least fix-point so obtained is inconsistent, then the approach fails and no meaning is attached to the program. This paper introduces several approaches to considering consistence (under the term coherence) into a fuzzy setting, and studies some of their properties.

Citation

Please, cite this work as:

[MO09] N. Madrid and M. Ojeda-Aciego. “On the measure of incoherence in extended residuated logic programs”. In: FUZZ-IEEE 2009, IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 20-24 August 2009, Proceedings. IEEE, 2009, pp. 598-603. DOI: 10.1109/FUZZY.2009.5277277. URL: https://doi.org/10.1109/FUZZY.2009.5277277.

BibTeX

@InProceedings{Madrid2009,
     author = {Nicol{’a}s Madrid and Manuel Ojeda-Aciego},
     booktitle = {{FUZZ-IEEE} 2009, {IEEE} International Conference on Fuzzy Systems, Jeju Island, Korea, 20-24 August 2009, Proceedings},
     title = {On the measure of incoherence in extended residuated logic programs},
     year = {2009},
     pages = {598–603},
     publisher = {{IEEE}},
     bibsource = {dblp computer science bibliography, https://dblp.org},
     biburl = {https://dblp.org/rec/conf/fuzzIEEE/MadridO09.bib},
     doi = {10.1109/FUZZY.2009.5277277},
     timestamp = {Mon, 03 Jan 2022 00:00:00 +0100},
     url = {https://doi.org/10.1109/FUZZY.2009.5277277},
}

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On the measure of incoherence in extended residuated logic programs

Cites

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Papers citing this work

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

[1] H. Bustince, N. Madrid, and M. Ojeda-Aciego. “The Notion of Weak-Contradiction: Definition and Measures”. In: IEEE Transactions on Fuzzy Systems 23.4 (Aug. 2015), p. 1057–1069. ISSN: 1941-0034. DOI: 10.1109/tfuzz.2014.2337934. URL: http://dx.doi.org/10.1109/tfuzz.2014.2337934.

[2] 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.

[3] M. E. Cornejo, D. Lobo, and J. Medina. “Selecting the Coherence Notion in Multi-adjoint Normal Logic Programming”. In: Advances in Computational Intelligence. Springer International Publishing, 2017, p. 447–457. ISBN: 9783319591537. DOI: 10.1007/978-3-319-59153-7_39. URL: http://dx.doi.org/10.1007/978-3-319-59153-7_39.

[4] J. Janssen, S. Schockaert, D. Vermeir, et al. “A core language for fuzzy answer set programming”. In: International Journal of Approximate Reasoning 53.4 (Jun. 2012), p. 660–692. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2012.01.005. URL: http://dx.doi.org/10.1016/j.ijar.2012.01.005.

[5] N. Madrid and M. Ojeda-Aciego. “Measuring Inconsistency in Fuzzy Answer Set Semantics”. In: IEEE Transactions on Fuzzy Systems 19.4 (Aug. 2011), p. 605–622. ISSN: 1941-0034. DOI: 10.1109/tfuzz.2011.2114669. URL: http://dx.doi.org/10.1109/tfuzz.2011.2114669.

[6] N. Madrid and M. Ojeda-Aciego. “Measuring instability in normal residuated logic programs: Adding information”. In: International Conference on Fuzzy Systems. IEEE, Jul. 2010, p. 1–7. DOI: 10.1109/fuzzy.2010.5584819. URL: http://dx.doi.org/10.1109/fuzzy.2010.5584819.

[7] N. Madrid and M. Ojeda-Aciego. “Measuring Instability in Normal Residuated Logic Programs: Discarding Information”. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods. Springer Berlin Heidelberg, 2010, p. 128–137. ISBN: 9783642140556. DOI: 10.1007/978-3-642-14055-6_14. URL: http://dx.doi.org/10.1007/978-3-642-14055-6_14.

[8] N. Madrid and M. Ojeda-Aciego. “On the measure of incoherent information in extended multi-adjoint logic programs”. In: 2013 IEEE Symposium on Foundations of Computational Intelligence (FOCI). IEEE, Apr. 2013, p. 30–37. DOI: 10.1109/foci.2013.6602452. URL: http://dx.doi.org/10.1109/foci.2013.6602452.

[9] 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.