An implementation of a dual tableaux system for order-of-magnitude qualitative reasoning

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Authors

Alfredo Burrieza

Ángel Mora

Manuel Ojeda-Aciego

Ewa Orlowska

Published

1 January 2009

Publication details

Int. J. Comput. Math. vol. 86 (10{&}11), pages 1852–1866.

Links

Abstract

Abstract Logic programming has been used as a natural framework to automate deduction in the logic of order-of-magnitude reasoning. Specifically, we introduce a Prolog implementation of the Rasiowa–Sikorski proof system associated with the relational translation Re(OM) of the multi-modal logic of order-of-magnitude qualitative reasoning OM. Keywords: relational theorem provingRasiowa–Sikorski proceduremodal logictableaux procedureautomated theorem proving 2000 AMS Subject Classifications : 03B4505E1068T15 Acknowledgements The author A. Mora was partially supported by P06-FQM-02049, and the author M. Ojeda-Aciego was partially supported by TIC06-15455-C03-01. The authors acknowledge the anonymous referees for providing valuable suggestions on how to improve the final version of this article. Notes The full implementation (developed in SWI-Prolog Version 5.6.33 for Windows platform) is available from the address http://homepage.mac.com/alicauchy/ The full trace of execution of the procedure applied on all the axioms of Citation5 can be obtained from the address http://homepage.mac.com/alicauchy/

Citation

Please, cite this work as:

[Bur+09] A. Burrieza, Á. Mora, M. Ojeda-Aciego, et al. “An implementation of a dual tableaux system for order-of-magnitude qualitative reasoning”. In: Int. J. Comput. Math. 86.10&11 (2009), pp. 1852-1866. DOI: 10.1080/00207160902777906. URL: https://doi.org/10.1080/00207160902777906.

BibTeX

@Article{Burrieza2009b,
     author = {Alfredo Burrieza and {’A}ngel Mora and Manuel Ojeda-Aciego and Ewa Orlowska},
     journal = {Int. J. Comput. Math.},
     title = {An implementation of a dual tableaux system for order-of-magnitude qualitative reasoning},
     year = {2009},
     number = {10{&}11},
     pages = {1852–1866},
     volume = {86},
     bibsource = {dblp computer science bibliography, https://dblp.org},
     biburl = {https://dblp.org/rec/journals/ijcm/BurriezaMOO09.bib},
     doi = {10.1080/00207160902777906},
     timestamp = {Fri, 23 Sep 2022 01:00:00 +0200},
     url = {https://doi.org/10.1080/00207160902777906},
}

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An implementation of a dual tableaux system for order-of-magnitude qualitative reasoning

Cites

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Papers citing this work

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

[1] A. Formisano, E. G. Omodeo, and A. Policriti. “Reasoning on Relations, Modalities, and Sets”. In: Ewa Orłowska on Relational Methods in Logic and Computer Science. Springer International Publishing, 2018, p. 129–168. ISBN: 9783319978796. DOI: 10.1007/978-3-319-97879-6_6. URL: http://dx.doi.org/10.1007/978-3-319-97879-6_6.

[2] J. Goli ska-Pilarek and E. Munoz-Velasco. “A hybrid qualitative approach for relative movements”. In: Logic Journal of IGPL 23.3 (Apr. 2015), p. 410–420. ISSN: 1368-9894. DOI: 10.1093/jigpal/jzv012. URL: http://dx.doi.org/10.1093/jigpal/jzv012.

[3] J. Golińska-Pilarek, A. Mora, and E. Muñoz-Velasco. “An ATP of a Relational Proof System for Order of Magnitude Reasoning with Negligibility, Non-closeness and Distance”. In: PRICAI 2008: Trends in Artificial Intelligence. Springer Berlin Heidelberg, 2008, p. 128–139. ISBN: 9783540891970. DOI: 10.1007/978-3-540-89197-0_15. URL: http://dx.doi.org/10.1007/978-3-540-89197-0_15.

[4] J. Golińska-Pilarek and E. Muñoz-Velasco. “Reasoning with Qualitative Velocity: Towards a Hybrid Approach”. In: Hybrid Artificial Intelligent Systems. Springer Berlin Heidelberg, 2012, p. 635–646. ISBN: 9783642289422. DOI: 10.1007/978-3-642-28942-2_57. URL: http://dx.doi.org/10.1007/978-3-642-28942-2_57.

[5] J. Golinska-Pilarek, E. Munoz-Velasco, and A. Mora. “A new deduction system for deciding validity in modal logic K”. In: Logic Journal of IGPL 19.2 (Jul. 2010), p. 425–434. ISSN: 1368-9894. DOI: 10.1093/jigpal/jzq033. URL: http://dx.doi.org/10.1093/jigpal/jzq033.

[6] J. Golińska-Pilarek and E. Orłowska. “Dual tableau for monoidal triangular norm logic MTL”. In: Fuzzy Sets and Systems 162.1 (Jan. 2011), p. 39–52. ISSN: 0165-0114. DOI: 10.1016/j.fss.2010.09.007. URL: http://dx.doi.org/10.1016/j.fss.2010.09.007.

[7] J. Golińska-Pilarek and M. Zawidzki. “Everything is a Relation: A Preview”. In: Ewa Orłowska on Relational Methods in Logic and Computer Science. Springer International Publishing, 2018, p. 3–24. ISBN: 9783319978796. DOI: 10.1007/978-3-319-97879-6_1. URL: http://dx.doi.org/10.1007/978-3-319-97879-6_1.

[8] N. Madrid and M. Ojeda-Aciego. “On the existence and unicity of stable models in normal residuated logic programs”. In: International Journal of Computer Mathematics 89.3 (Feb. 2012), p. 310–324. ISSN: 1029-0265. DOI: 10.1080/00207160.2011.580842. URL: http://dx.doi.org/10.1080/00207160.2011.580842.

[9] A. Mora, E. Muñoz-Velasco, and J. Golińska-Pilarek. “Implementing a relational theorem prover for modal logic”. In: International Journal of Computer Mathematics 88.9 (Jun. 2011), p. 1869–1884. ISSN: 1029-0265. DOI: 10.1080/00207160.2010.493211. URL: http://dx.doi.org/10.1080/00207160.2010.493211.