Investigation of a Mathematical System for Decision-Making Machines. (Relations Between Logical Structure, Time and Natural Numbers).
Final rept. 15 Oct 57-31 Dec 70,
ILLINOIS UNIV URBANA BIOLOGICAL COMPUTER LAB
Pagination or Media Count:
The investigation of the theory of natural numbers as mapped onto kenogrammatic and many-valued systems was continued. The following conclusion was reached Whereas natural numbers composed against the background of two-valued, classic logic permit only one basic mode of composition, the very same numbers when exposed to the laws of a trans-classic logic require a minimum of four basic modes of composition. Three of them form a systematic group, but an additional one has to be defined separately. The systemic group derives its existence from the fact that numbers are mapped onto purely kenogrammatic structures. A third mode of composition is possible where any sort of structural property belonging to a given number has to play a relevant part in the compositional procedure. This was called trito-composition. It was discovered that the three main types of kenogrammatic compositions of natural numbers yielded a general frame within which for proto-, deutero- and trito-structures separately arithmetical subroutines could be located with increased with asending natural numbers to practically infinite complexity. Author
- Theoretical Mathematics