On Solutions to the Set-Theoretical Yang-Baxter Equation in Wajsberg-Algebras

Oner, Tahsin; Katican, Tugce

doi:10.3390/axioms7010006

Cited by 9 publications

(5 citation statements)

References 24 publications

(17 reference statements)

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“…The Yang-Baxter equation guarantees that the order in which we start this analysis is not important (see [56]). How to obtain solutions for set-theoretic Yang-Baxter equations in a context of Boole or Heyting Algebras is also indicated in [52,57,58], or even in [59].…”

Section: Remark 19mentioning

confidence: 99%

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

et al. 2021

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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.

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Section: Remark 19mentioning

confidence: 99%

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

et al. 2021

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“…As we continued our work on unification theories begun in previous papers (see, for example, [2,4,7,9,10]), the unification approaches led us to new results. The Yang-Baxter equation (see [11][12][13][14]) can be interpreted in terms of logical circuits and, in logic, it represents a kind of compatibility condition when working with many logical sentences at the same time. In this type of logic, we work at the same time with sentences that contradict each other.…”

Section: Final Comments and Implicationsmentioning

confidence: 99%

Unification Theories: Means and Generalized Euler Formulas

Iordanescu

Nichita

Pasarescu

2020

Axioms

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“…The sections of the current paper contain not only examples of unification structures in mathematics, but also various versions of the Yang-Baxter equation. This paper could be extended to a discussion about Logic [32][33][34], Machine Learning [35,36], transcendence and transcendental numbers [23,37], transdisciplinarity [38][39][40], etc.…”

Section: Relationship With Poetrymentioning

confidence: 99%

Mathematics and Poetry • Unification, Unity, Union

Nichita¹

2020

Sci

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We consider a multitude of topics in mathematics where unification constructions play an important role: the Yang–Baxter equation and its modified version, Euler’s formula for dual numbers, means and their inequalities, topics in differential geometry, etc. It is interesting to observe that the idea of unification (unity and union) is also present in poetry. Moreover, Euler’s identity is a source of inspiration for the post-modern poets.

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On Solutions to the Set-Theoretical Yang-Baxter Equation in Wajsberg-Algebras

Abstract: Abstract:In this work, we introduce Wajsberg algebras which are equivalent structures to MV-algebras in their implicational version, and then we define new notions and give new solutions to the set-theoretical Yang-Baxter equation by using Wajsberg algebras.

Cited by 9 publications

References 24 publications

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

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

Unification Theories: Means and Generalized Euler Formulas

Mathematics and Poetry • Unification, Unity, Union

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