Research Article
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Year 2021, , 41 - 49, 22.03.2021
https://doi.org/10.32323/ujma.738463

Abstract

References

  • [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.
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  • [12] R. Carbo-Dorca, J. Math. Chem., 56(2018), 1353-1356.
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  • [14] L.A. Zadeh, Information and Control, 8(1965), 338-353.
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  • [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).
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  • [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

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

Abstract

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.

References

  • [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).
There are 35 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ramon Carbó-dorca

Publication Date March 22, 2021
Submission Date May 16, 2020
Acceptance Date March 12, 2021
Published in Issue Year 2021

Cite

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. March 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, no. 1 (March 2021): 41-49. https://doi.org/10.32323/ujma.738463.
EndNote Carbó-dorca R (March 1, 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., vol. 4, no. 1, pp. 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 (March 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, vol. 4, no. 1, 2021, pp. 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.

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