We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Applications of Non-Standard analysis in Topoi to Mathematical Neurosciences and Artificial Intelligence: Infons, Energons, Receptons (I).
- Authors
Badea, Ileana Ruxandra; Mocanu, Carmen Elena; Nichita, Florin F.; Păsărescu, Ovidiu
- 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.
- Subjects
NONSTANDARD mathematical analysis; ARTIFICIAL intelligence; MATHEMATICAL analysis; YANG-Baxter equation; SET theory
- Publication
Mathematics (2227-7390), 2021, Vol 9, Issue 17, p2048
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math9172048