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

Ramon Carbó-dorca

doi:10.32323/ujma.738463

EN

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

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.

Keywords

Fuzzy Sets, Fuzzy Logic, Tagged Sets, Boolean Tags, Logical Tags, Boolean Tagged Sets, Boolean Hypercubes, Concatenation of Boolean Hypercubes, Natural Number Recursion, Mersenne Numbers, Multivalued Logic, Gödel-like Properties of Boolean Sets, Artificial Intelligence

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Ramon Carbó-dorca ^*
Spain

Publication Date

March 22, 2021

Submission Date

May 16, 2020

Acceptance Date

March 12, 2021

Published in Issue

Year 2021 Volume: 4 Number: 1

DOI

https://doi.org/10.32323/ujma.738463

IZ

https://izlik.org/JA79RT33NR

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

1.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):41-49. doi:10.32323/ujma.738463

Chicago

Carbó-dorca, Ramon. 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.

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

[1]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, Mar. 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 1, 2021): 41-49. https://doi.org/10.32323/ujma.738463.

JAMA

1.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, Mar. 2021, pp. 41-49, doi:10.32323/ujma.738463.

Vancouver

1.Ramon Carbó-dorca. Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence. Univ. J. Math. Appl. 2021 Mar. 1;4(1):41-9. doi:10.32323/ujma.738463