Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, , 41 - 49, 22.03.2021
https://doi.org/10.32323/ujma.738463

Öz

Kaynakça

  • [1] R. Carbo-Dorca, Fuzzy sets and boolean tagged sets, J. Math. Chem., 22(1997), 143-147.
  • [2] R. Carbo-Dorca,Fuzzy sets and Boolean tagged sets, vector semispaces and convex sets, QSM and ASA density functions, diagonal vector spaces and quantum chemistry, Adv. Molec. Simil., 2(1998), 43-72.
  • [3] R. Carbo-Dorca, N-dimensional Boolean hypercubes and the Goldbach conjecture, J. Math. Chem., 54(2016), 1213-1220.
  • [4] R. Carbo-Dorca, Natural vector spaces, (inward power and Minkowski norm of a natural vector, natural Boolean hypercubes) and Fermat’s last theorem, J. Math. Chem., 55(2017), 914-940.
  • [5] R. Carbo-Dorca, Boolean hypercubes as time representation holders, J. Math. Chem., 56(2018), 1349-1352.
  • [6] R. Carbo-Dorca, Boolean hypercubes and the structure of vector spaces, J. Math. Sci. Model., 1(2018), 1-14.
  • [7] R. Carbo-Dorca, Transformation of Boolean hypercube vertices into unit interval elements: QSPR workout consequences, J., Math. Chem., 57(2019), 694-696.
  • [8] R. Carbo-Dorca, Role of the structure of Boolean hypercubes when used as vectors in natural (Boolean) vector semispaces, J. Math. Chem., 57(2019), 697-700.
  • [9] R. Carbo-Dorca, Cantor-like infinity sequences and Gödel-like incompleteness revealed by means of Mersenne infinite dimensional Boolean hypercube concatenation, J. Math. Chem., 58(2020), 1-5.
  • [10] R. Carbo-Dorca, Boolean Hypercubes, Mersenne numbers and the Collatz conjecture Research Gate Preprint DOI:10.13140/RG.2.2.28323.40482.
  • [11] R. Carbo-Dorca, T. Chakraborty, J. Comp. Chem., 40(2019), 2653-2653.
  • [12] R. Carbo-Dorca, J. Math. Chem., 56(2018), 1353-1356.
  • [13] M. Bunge, Matter and Mind. A Philosophical Inquiry, Boston Studies in the Philosophy of Science, Vol 287, Springer (Dordrecht) (2010).
  • [14] L.A. Zadeh, Information and Control, 8(1965), 338-353.
  • [15] https://en.wikipedia.org/wiki/Fuzzy_set
  • [16] E. A. J. Sloane(Editor), Online Encyclopedia of Integer Sequences, https://oeis.org/wiki/Welcome, Sequence A083318.
  • [17] P.Jaccard, Bulletin de la Societe Vaudoise des Sciences Naturelles, 37(1901), 547-579.
  • [18] P.Jaccard, New Phytologist, 11(1912), 37-50.
  • [19] T.T. Tanimoto, An Elementary Mathematical theory of Classification and Prediction ,Internal IBM Technical Report, (1958).
  • [20] D. J. Rogers, T. T. Tanimoto, Science, 132(1960), 1115-1118.
  • [21] J. T. Tou, R. C. Gonzalez, Pattern Recognition Principles, Addison-Wesley Pub. Co. Reading Mass., USA (1974).
  • [22] A. Racz A, D. Bajusz, Heberger, J. Cheminform., 10(2018), 48, https://doi.org/10.1186/s13321-018-0302-y.
  • [23] S. Gottwald S, Many-Valued Logic, http://plato.stanford.edu/entries/logic-manyvalued/, Stanford Encyclopedia of Philosophy, Metaphysics Research Lab, Stanford University (2009).
  • [24] https://en.wikipedia.org/wiki/Artificial_intelligence#Tools
  • [25] J. Devillers (Editor), Neural Networks in QSAR and Drug Design, Vol 2 in the Series: Principles of QSAR and Drug Design, Academic Press, San Diego, (1996).
  • [26] A. M. Virshup, J. Contreras-Garc´ıa, P. Wipf P, W. Yang W, D. N. Beratan, J. Am. Chem. Soc., 135(2013), 7296-7303.
  • [27] L. K. Boerner (Editor), Artificial Intelligence in Drug Discovery, Chemical and Engineering News Discovery Report, American Chemical Society (2019).
  • [28] A. Acharya, R. Agarwal, M. B. Baker, J. Baudry, D. Bhowmik, S. Boehm, K. G. Byler, S. Y. Chen, L. Coates, C. J. Cooper, O. Demerdash, I. Daidone, J. D. Eblen, S. Ellingson, S. Forli, J. Glaser, J. C. Gumbart, J. Gunnels, O. Hernandez, S. Irle, D. W. Kneller, A. Kovalevsky, J. Larkin, T. J. Lawrence, S. LeGrand, S.-H. Liu, J.C. Mitchell, G. Park, J.M. Parks, A. Pavlova, L. Petridis, D. Poole, L. Pouchard, A. Ramanathan, D. M. Rogers, D. Santos-Martins, A. Scheinberg, A. Sedova, Y. Shen, J. C. Smith, M. D. Smith, C. Soto, A. Tsaris, M. Thavappiragasam, A. F. Tillack, J. V. Vermaas, V. Q. Vuong, J. Yin, S. Yoo, M. Zahran, L. Zanetti-Polzi, Supercomputer-Based Ensemble Docking Drug Discovery Pipeline with Application to Covid-19, J. Chem. Inf. Model., 60(2020), 5832-5852.
  • [29] R. Carbo-Dorca, J. Math. Chem., 51(2013), 413-419.
  • [30] https://deepmind.com/blog/article/alphafold-a-solution-to-a-50-year-old-grand-challenge-in-biology.
  • [31] J. Hermann, J. Sch¨atzle, F. Noe, Deep-Neural-Network Solution of the Electronic Schr¨odinger Equation, Nature Chemistry, 12(2020), 891-897.
  • [32] L. Reyzin, Unprovability comes to machine learning, Nature 65(2019), 166-167.
  • [33] M. Bunge, Causality and Modern Science, Dover Publications (New York) 3rd Revised Edition, 2011.
  • [34] K. Godel K, Monatsh. Math., 38(1931),173-198.
  • [35] J. Chang, R. Carb´o-Dorca, Fuzzy Hypercubes and their Time-Like Evolution, Research Gate Preprint: DOI: 10.13140/RG.2.2.26064.25605 (2020).

Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence

Yıl 2021, , 41 - 49, 22.03.2021
https://doi.org/10.32323/ujma.738463

Öz

Boolean and logical hypercubes are discussed as providers of tags to logical object sets, transforming them into logical tagged sets, a generalization of fuzzy sets. The equivalence of Boolean and logical sets permits to consider natural tags as an equivalent basis of logical tagged sets. Boolean hypercube concatenation easily allows studying how Boolean information is transmitted. From there a Gödel-like behavior of Boolean hypercubes and thus of logical object sets can be unveiled. Later, it is discussed the iterative building of natural numbers, considering Mersenne numbers as upper bounds of this kind of recursive construction. From there information acquisition, recursive logic, and artificial intelligence are also examined.

Kaynakça

  • [1] R. Carbo-Dorca, Fuzzy sets and boolean tagged sets, J. Math. Chem., 22(1997), 143-147.
  • [2] R. Carbo-Dorca,Fuzzy sets and Boolean tagged sets, vector semispaces and convex sets, QSM and ASA density functions, diagonal vector spaces and quantum chemistry, Adv. Molec. Simil., 2(1998), 43-72.
  • [3] R. Carbo-Dorca, N-dimensional Boolean hypercubes and the Goldbach conjecture, J. Math. Chem., 54(2016), 1213-1220.
  • [4] R. Carbo-Dorca, Natural vector spaces, (inward power and Minkowski norm of a natural vector, natural Boolean hypercubes) and Fermat’s last theorem, J. Math. Chem., 55(2017), 914-940.
  • [5] R. Carbo-Dorca, Boolean hypercubes as time representation holders, J. Math. Chem., 56(2018), 1349-1352.
  • [6] R. Carbo-Dorca, Boolean hypercubes and the structure of vector spaces, J. Math. Sci. Model., 1(2018), 1-14.
  • [7] R. Carbo-Dorca, Transformation of Boolean hypercube vertices into unit interval elements: QSPR workout consequences, J., Math. Chem., 57(2019), 694-696.
  • [8] R. Carbo-Dorca, Role of the structure of Boolean hypercubes when used as vectors in natural (Boolean) vector semispaces, J. Math. Chem., 57(2019), 697-700.
  • [9] R. Carbo-Dorca, Cantor-like infinity sequences and Gödel-like incompleteness revealed by means of Mersenne infinite dimensional Boolean hypercube concatenation, J. Math. Chem., 58(2020), 1-5.
  • [10] R. Carbo-Dorca, Boolean Hypercubes, Mersenne numbers and the Collatz conjecture Research Gate Preprint DOI:10.13140/RG.2.2.28323.40482.
  • [11] R. Carbo-Dorca, T. Chakraborty, J. Comp. Chem., 40(2019), 2653-2653.
  • [12] R. Carbo-Dorca, J. Math. Chem., 56(2018), 1353-1356.
  • [13] M. Bunge, Matter and Mind. A Philosophical Inquiry, Boston Studies in the Philosophy of Science, Vol 287, Springer (Dordrecht) (2010).
  • [14] L.A. Zadeh, Information and Control, 8(1965), 338-353.
  • [15] https://en.wikipedia.org/wiki/Fuzzy_set
  • [16] E. A. J. Sloane(Editor), Online Encyclopedia of Integer Sequences, https://oeis.org/wiki/Welcome, Sequence A083318.
  • [17] P.Jaccard, Bulletin de la Societe Vaudoise des Sciences Naturelles, 37(1901), 547-579.
  • [18] P.Jaccard, New Phytologist, 11(1912), 37-50.
  • [19] T.T. Tanimoto, An Elementary Mathematical theory of Classification and Prediction ,Internal IBM Technical Report, (1958).
  • [20] D. J. Rogers, T. T. Tanimoto, Science, 132(1960), 1115-1118.
  • [21] J. T. Tou, R. C. Gonzalez, Pattern Recognition Principles, Addison-Wesley Pub. Co. Reading Mass., USA (1974).
  • [22] A. Racz A, D. Bajusz, Heberger, J. Cheminform., 10(2018), 48, https://doi.org/10.1186/s13321-018-0302-y.
  • [23] S. Gottwald S, Many-Valued Logic, http://plato.stanford.edu/entries/logic-manyvalued/, Stanford Encyclopedia of Philosophy, Metaphysics Research Lab, Stanford University (2009).
  • [24] https://en.wikipedia.org/wiki/Artificial_intelligence#Tools
  • [25] J. Devillers (Editor), Neural Networks in QSAR and Drug Design, Vol 2 in the Series: Principles of QSAR and Drug Design, Academic Press, San Diego, (1996).
  • [26] A. M. Virshup, J. Contreras-Garc´ıa, P. Wipf P, W. Yang W, D. N. Beratan, J. Am. Chem. Soc., 135(2013), 7296-7303.
  • [27] L. K. Boerner (Editor), Artificial Intelligence in Drug Discovery, Chemical and Engineering News Discovery Report, American Chemical Society (2019).
  • [28] A. Acharya, R. Agarwal, M. B. Baker, J. Baudry, D. Bhowmik, S. Boehm, K. G. Byler, S. Y. Chen, L. Coates, C. J. Cooper, O. Demerdash, I. Daidone, J. D. Eblen, S. Ellingson, S. Forli, J. Glaser, J. C. Gumbart, J. Gunnels, O. Hernandez, S. Irle, D. W. Kneller, A. Kovalevsky, J. Larkin, T. J. Lawrence, S. LeGrand, S.-H. Liu, J.C. Mitchell, G. Park, J.M. Parks, A. Pavlova, L. Petridis, D. Poole, L. Pouchard, A. Ramanathan, D. M. Rogers, D. Santos-Martins, A. Scheinberg, A. Sedova, Y. Shen, J. C. Smith, M. D. Smith, C. Soto, A. Tsaris, M. Thavappiragasam, A. F. Tillack, J. V. Vermaas, V. Q. Vuong, J. Yin, S. Yoo, M. Zahran, L. Zanetti-Polzi, Supercomputer-Based Ensemble Docking Drug Discovery Pipeline with Application to Covid-19, J. Chem. Inf. Model., 60(2020), 5832-5852.
  • [29] R. Carbo-Dorca, J. Math. Chem., 51(2013), 413-419.
  • [30] https://deepmind.com/blog/article/alphafold-a-solution-to-a-50-year-old-grand-challenge-in-biology.
  • [31] J. Hermann, J. Sch¨atzle, F. Noe, Deep-Neural-Network Solution of the Electronic Schr¨odinger Equation, Nature Chemistry, 12(2020), 891-897.
  • [32] L. Reyzin, Unprovability comes to machine learning, Nature 65(2019), 166-167.
  • [33] M. Bunge, Causality and Modern Science, Dover Publications (New York) 3rd Revised Edition, 2011.
  • [34] K. Godel K, Monatsh. Math., 38(1931),173-198.
  • [35] J. Chang, R. Carb´o-Dorca, Fuzzy Hypercubes and their Time-Like Evolution, Research Gate Preprint: DOI: 10.13140/RG.2.2.26064.25605 (2020).
Toplam 35 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Ramon Carbó-dorca

Yayımlanma Tarihi 22 Mart 2021
Gönderilme Tarihi 16 Mayıs 2020
Kabul Tarihi 12 Mart 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Carbó-dorca, R. (2021). Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence. Universal Journal of Mathematics and Applications, 4(1), 41-49. https://doi.org/10.32323/ujma.738463
AMA Carbó-dorca R. Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence. Univ. J. Math. Appl. Mart 2021;4(1):41-49. doi:10.32323/ujma.738463
Chicago Carbó-dorca, Ramon. “Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence”. Universal Journal of Mathematics and Applications 4, sy. 1 (Mart 2021): 41-49. https://doi.org/10.32323/ujma.738463.
EndNote Carbó-dorca R (01 Mart 2021) Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence. Universal Journal of Mathematics and Applications 4 1 41–49.
IEEE R. Carbó-dorca, “Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence”, Univ. J. Math. Appl., c. 4, sy. 1, ss. 41–49, 2021, doi: 10.32323/ujma.738463.
ISNAD Carbó-dorca, Ramon. “Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence”. Universal Journal of Mathematics and Applications 4/1 (Mart 2021), 41-49. https://doi.org/10.32323/ujma.738463.
JAMA Carbó-dorca R. Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence. Univ. J. Math. Appl. 2021;4:41–49.
MLA Carbó-dorca, Ramon. “Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence”. Universal Journal of Mathematics and Applications, c. 4, sy. 1, 2021, ss. 41-49, doi:10.32323/ujma.738463.
Vancouver Carbó-dorca R. Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence. Univ. J. Math. Appl. 2021;4(1):41-9.

 23181

Universal Journal of Mathematics and Applications 

29207              

Creative Commons License  The published articles in UJMA are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.