Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence
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 hy...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Emrah Evren KARA
2021-03-01
|
| Series: | Universal Journal of Mathematics and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/1106979 |
| _version_ | 1797350179372793856 |
|---|---|
| author | Ramon Carbó-dorca |
| author_facet | Ramon Carbó-dorca |
| author_sort | Ramon Carbó-dorca |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T12:42:05Z |
| format | Article |
| id | doaj.art-141a09e430b345fa82e11a05fb4b1dd7 |
| institution | Directory Open Access Journal |
| issn | 2619-9653 |
| language | English |
| last_indexed | 2024-03-08T12:42:05Z |
| publishDate | 2021-03-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj.art-141a09e430b345fa82e11a05fb4b1dd72024-01-21T09:05:43ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532021-03-0141414910.32323/ujma.7384631225Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial IntelligenceRamon Carbó-dorca0University of GironaBoolean 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.https://dergipark.org.tr/tr/download/article-file/1106979fuzzy sets fuzzy logictagged setsboolean tagslogical tagsboolean tagged setsboolean hypercubesconcatenation of boolean hypercubesnatural number recursionmersenne numbersmultivalued logicgödel-like properties of boolean setsartificial intelligence |
| spellingShingle | Ramon Carbó-dorca Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence Universal Journal of Mathematics and Applications 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 |
| title | Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence |
| title_full | Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence |
| title_fullStr | Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence |
| title_full_unstemmed | Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence |
| title_short | Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence |
| title_sort | boolean hypercubes the origin of a tagged recursive logic and the limits of artificial intelligence |
| topic | 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 |
| url | https://dergipark.org.tr/tr/download/article-file/1106979 |
| work_keys_str_mv | AT ramoncarbodorca booleanhypercubestheoriginofataggedrecursivelogicandthelimitsofartificialintelligence |