Applications of Non-Standard analysis in Topoi to Mathematical Neurosciences and Artificial Intelligence: Infons, Energons, Receptons (I)
| Autor: | Ileana Ruxandra Badea, Ovidiu Pasarescu, Florin F. Nichita, Carmen Elena Mocanu |
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| Rok vydání: | 2021 |
| Předmět: |
brain studies
Class (set theory) Computer science General Mathematics media_common.quotation_subject MathematicsofComputing_GENERAL Intuitionistic logic intuitionistic logic Topos theory Non-standard analysis non-standard analysis topos theory artificial intelligence Yang–Baxter equations QA1-939 Computer Science (miscellaneous) Engineering (miscellaneous) media_common business.industry Internal set theory Special class Computer Science::Programming Languages Artificial intelligence Consciousness business Mathematics |
| Zdroj: | Mathematics, Vol 9, Iss 2048, p 2048 (2021) Mathematics; Volume 9; Issue 17; Pages: 2048 |
| ISSN: | 2227-7390 |
| DOI: | 10.3390/math9172048 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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