Axioms of Soft Logic

Moshe Klein*, Oded Maimon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this paper, we develop the foundation of a new mathematical language, which we term “Soft Logic”. This language enables us to present an extension of the number 0 from a singular point to a continuous line. We create a distinction between −0 and +0 and generate a new type of numbers, which we call ‘Bridge Numbers’ (BN): a0¯⊥b1¯, where a, b are real numbers, “a” is the value on the 0¯ axis, and “b” is the value on the 1¯ axis. We proceed by defining arithmetic and algebraic operations on the Bridge Numbers, investigate their properties, and conclude by defining goals for further research. In the Attachment, we continue comparing our results with existing mathematical work on Infinitesimals, Dual numbers, and Nonstandard analysis. The research is a part of “Digital living 2030” project with Stanford University.

Original languageEnglish
Pages (from-to)205-215
Number of pages11
JournalP-Adic Numbers, Ultrametric Analysis, and Applications
Issue number3
StatePublished - 1 Jul 2019


FundersFunder number
Koret Foundation


    • dual numbers
    • infinitesimal
    • nonstandard analysis
    • p-adic numbers
    • soft logic


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