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Computing Duals of Finite Gödel Algebras

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Konferencja
Federated Conference on Computer Science and Information Systems (15 ; 06-09.09.2020 ; Sofia, Bulgaria)
Języki publikacji
EN
Abstrakty
EN
We introduce an algorithm that computes and counts the duals of finite G\"odel-Dummett algebras of k ≥ 1 elements. The computational cost of our algorithm depends on the factorization of k, nevertheless a Python implementation is sufficiently fast to compute the results for very large values of k.
Rocznik
Tom
Strony
31--34
Opis fizyczny
Bibliogr. 27 poz., wz., tab.
Twórcy
  • Dipartimento di Informatica, Università degli Studi di Milano, Italy
  • Dipartimento di Informatica, Università degli Studi di Milano, Italy
autor
  • Dipartimento di Informatica, Università degli Studi di Milano, Italy
Bibliografia
  • 1. N. Smith, “Fuzzy logics in theories of vagueness,” in Handbook of Mathematical Fuzzy Logic. Vol. 3, P. Cintula, C. Fermüller, and C. Noguera, Eds. College Publications, 2016, vol. 58, pp. 1237–1281.
  • 2. P. Hájek, Metamathematics of Fuzzy Logic, ser. Trends in Logic. Kluwer Academic Publishers, 1998, vol. 4.
  • 3. K. Gödel, “Zum intuitionistischen Aussagenkalkul,” Anzeiger Akademie der Wissenschaften Wien, vol. 69, pp. 65–66, 1932.
  • 4. M. Dummett, “A propositional calculus with denumerable matrix,” J. Symb. Log., vol. 24, no. 2, pp. 97–106, 1959.
  • 5. A. Horn, “Free L-Algebras,” J. Symb. Log., vol. 34, no. 3, pp. 475–480, 1969.
  • 6. O. M. D’Antona and V. Marra, “Computing coproducts of finitely presented Gödel algebras,” Ann. Pure Appl. Logic, vol. 142, no. 1, pp. 202–211, 2006.
  • 7. W. Taylor, “The fine spectrum of a variety,” Algebra Universalis, vol. 5, no. 1, pp. 263–303, 1975.
  • 8. D. Valota, “Spectra of Gödel Algebras,” in Language, Logic, and Computation. TbiLLC 2017, ser. Lecture Notes in Computer Science, A. Silva, S. Staton, P. Sutton, and C. Umbach, Eds., 2019, vol. 11456.
  • 9. W. McCune, “Prover9 and mace4,” 2005–2010, http://www.cs.unm.edu/~mccune/prover9/.
  • 10. J. A. Robinson and A. Voronkov, Eds., Handbook of Automated Reasoning (in 2 volumes). Elsevier and MIT Press, 2001.
  • 11. S. Aguzzoli and P. Codara, “Recursive formulas to compute coproducts of finite Gödel algebras and related structures,” in 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2016, pp. 201–208.
  • 12. A. Horn, “Logic with Truth Values in a Linearly Ordered Heyting Algebra,” J. Symb. Log., vol. 34, no. 3, pp. pp. 395–408, 1969.
  • 13. S. Aguzzoli, S. Bova, and B. Gerla, “Free Algebras and Functional Representation for Fuzzy Logics,” in Handbook of Mathematical Fuzzy Logic, P. Cintula, P. Hájek, and C. Noguera, Eds. College Publications, 2011, vol. 2, pp. 713–791.
  • 14. A. Knopfmacher and M. E. Mays, “A survey of factorization counting functions,” International Journal of Number Theory, vol. 01, no. 04, pp. 563–581, 2005.
  • 15. T. Cormen, C. Leiserson, R. Rivest, and C. Stein, Introduction To Algorithms. McGraw-Hill Publishing Company, 2001.
  • 16. F. Dodd and L. Mattics, “Estimating the number of multiplicative partitions,” Rocky Mountain Journal of Mathematics, vol. 17, no. 4, pp. 797–814, 12 1987.
  • 17. A. Meurer and et al., “Sympy: symbolic computing in python,” PeerJ Computer Science, vol. 3, p. e103, 2017. [Online]. Available: https://doi.org/10.7717/peerj-cs.103
  • 18. J. Ellson, E. R. Gansner, E. Koutsofios, S. C. North, and G. Woodhull, “Graphviz and dynagraph - static and dynamic graph drawing tools,” in GRAPH DRAWING SOFTWARE. Springer-Verlag, 2003, pp. 127–148.
  • 19. R. Belohlavek and V. Vychodil, “Residuated lattices of size ≤ 12,” Order, vol. 27, no. 2, pp. 147–161, 2010.
  • 20. F. Esteva and L. Godo, “Monoidal t-norm based logic: Towards a logic for left-continuous t-norms,” Fuzzy Sets and Systems, vol. 124, no. 3, pp. 271–288, 2001.
  • 21. S. Aguzzoli, M. Busaniche, and V. Marra, “Spectral Duality for Finitely Generated Nilpotent Minimum Algebras, with Applications,” J. Log. Comput., vol. 17, no. 4, pp. 749–765, 2007.
  • 22. S. Bova and D. Valota, “Finite RDP-algebras: Duality, Coproducts and Logic,” J. Log. Comput., vol. 22, no. 3, pp. 417–450, 2012.
  • 23. D. Valota, “Representations for logics and algebras related to revised drastic product t-norm,” Soft Computing, vol. 23, pp. 2331–2342, 2019.
  • 24. S. Aguzzoli, M. Bianchi, B. Gerla, and D. Valota, “Probability Measures in Gödel∆ Logic,” in Symbolic and Quantitative Approaches to Reasoning with Uncertainty, A. Antonucci, L. Cholvy, and O. Papini, Eds. Springer, 2017, pp. 353–363.
  • 25. S. Aguzzoli, M. Bianchi, B. Gerla, and D. Valota, “Free algebras, states and duality for the propositional Gödel∆ and Drastic Product logics,” International Journal of Approximate Reasoning, vol. 104, pp. 57–74, 2019.
  • 26. S. Aguzzoli, M. Bianchi, and D. Valota, “A note on Drastic Product logic,” in Information Processing and Management of Uncertainty, ser. Communications in Computer and Information Science, vol. 443. Springer, 2014, pp. 365–374.
  • 27. S. Aguzzoli, S. Bova, and D. Valota, “Free weak nilpotent minimum algebras,” Soft Computing, vol. 21, no. 1, pp. 79–95, 2017.
Uwagi
1. Track 1: Artificial Intelligence
2. Technical Session: 15th International Symposium Advances in Artificial Intelligence and Applications
3. Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-cb405b20-2d3a-4f95-9997-9532079bcf7e
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