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