TY - JOUR

T1 - Soft Logic as an Extension of Pascal’s Work

AU - Klein, Moshe

AU - Maimon, Oded

N1 - Publisher Copyright:
© 2023, Pleiades Publishing, Ltd.

PY - 2023/6

Y1 - 2023/6

N2 - Abstract: Pascal was a great mathematician and scientist, who contributed to many fields in mathematics and science. When he was 19 years old, he developed the first calculator, and together with Fermat he was the founder of probability theory. He investigated the properties of a triangle of numbers, which is named today “the Pascal triangle” and developed the method of proving theorems by mathematical induction. Pascal also investigated the properties of the cycloid, and he conducted the physical experiment that proved the existence of the void. After a spiritual experience at the age of 32, Pascal left mathematics and science altogether and dedicated himself to investigating and writing about religion. This paper suggests the new language of Soft logic, which is based on the extension of the number 0 to the zero axis. We conclude by an example of the extension of the Pascal Triangle with Soft numbers. Also, we discuss the possibility to develop a new model of computation.

AB - Abstract: Pascal was a great mathematician and scientist, who contributed to many fields in mathematics and science. When he was 19 years old, he developed the first calculator, and together with Fermat he was the founder of probability theory. He investigated the properties of a triangle of numbers, which is named today “the Pascal triangle” and developed the method of proving theorems by mathematical induction. Pascal also investigated the properties of the cycloid, and he conducted the physical experiment that proved the existence of the void. After a spiritual experience at the age of 32, Pascal left mathematics and science altogether and dedicated himself to investigating and writing about religion. This paper suggests the new language of Soft logic, which is based on the extension of the number 0 to the zero axis. We conclude by an example of the extension of the Pascal Triangle with Soft numbers. Also, we discuss the possibility to develop a new model of computation.

KW - Pascal

KW - arithmetic triangle

KW - binomial coefficient

KW - combinatorics

KW - probability

KW - soft logic

KW - soft numbers

UR - http://www.scopus.com/inward/record.url?scp=85166536789&partnerID=8YFLogxK

U2 - 10.1134/S207004662302005X

DO - 10.1134/S207004662302005X

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AN - SCOPUS:85166536789

SN - 2070-0466

VL - 15

SP - 119

EP - 132

JO - P-Adic Numbers, Ultrametric Analysis, and Applications

JF - P-Adic Numbers, Ultrametric Analysis, and Applications

IS - 2

ER -