Applications of Non-Standard analysis in Topoi to Mathematical Neurosciences and Artificial Intelligence: Infons, Energons, Receptons (I)

Ileana Ruxandra Badea, Carmen Elena Mocanu, Florin F. Nichita and Ovidiu Păsărescu
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Ileana Ruxandra Badea: The Faculty of Economic Cybernetics, Statistics and Informatics, The Bucharest University of Economical Studies, 15-17 Dorobanti Avenue, District 1, 010552 Bucharest, Romania
Carmen Elena Mocanu: Faculty of General Medicine, Carol Davila University of Medicine and Pharmacy, 8 Eroii Sanitari Avenue, District 5, 050474 Bucharest, Romania
Florin F. Nichita: Simion Stoilow Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, Romania
Ovidiu Păsărescu: Simion Stoilow Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, Romania

Mathematics, 2021, vol. 9, issue 17, 1-28

Abstract: The purpose of this paper is to promote new methods in mathematical modeling inspired by neuroscience—that is consciousness and subconsciousness—with an eye toward artificial intelligence as parts of the global brain. As a mathematical model, we propose topoi and their non-standard enlargements as models, due to the fact that their logic corresponds well to human thinking. For this reason, we built non-standard analysis in a special class of topoi; before now, this existed only in the topos of sets (A. Robinson). Then, we arrive at the pseudo-particles from the title and to a new axiomatics denoted by Intuitionistic Internal Set Theory ( IIST ); a class of models for it is provided, namely, non-standard enlargements of the previous topoi. We also consider the genetic–epigenetic interplay with a mathematical introduction consisting of a study of the Yang–Baxter equations with new mathematical results.

Keywords: non-standard analysis; topos theory; artificial intelligence; Yang–Baxter equations; brain studies; intuitionistic logic (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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