NeutroSemigroups Generated by Upside-Down Logic

Aykut Emniyet; Memet S¸ahin

Authors

Aykut Emniyet Department of Mathematics, Faculty of Engineering and Natural Sciences, Osmaniye Korkut Ata University, Osmaniye, T¨urkiye;
Memet S¸ahin Department of Mathematics, Gaziantep University, Gaziantep 27310, T¨urkiye;

Keywords:

NeutroSemigroup; Upside-Down Logic; Plithogenic Set; Contradiction Degree; NeutroAxiom; NeutroAlgebra

Abstract

Current models of NeutroAlgebras generally depend on static assignments to construct partial
axioms. This paper introduces a deterministic method to generate NeutroAlgebraic structures over plithogenic
spaces. We define a dual-threshold mode selector that combines the plithogenic intersection with the Three
Mode Upside-Down operator, strictly parameterized by the contradiction degree function. By introducing a
novel binary operation ⋆, we prove that the classical associative law fails within specific topological sub-regions
due to contradiction-triggered truth reversals. Since the associative property holds partially, fails partially,
and remains indeterminate elsewhere, the space equipped with ⋆ forms a NeutroSemigroup. This approach
provides a structural generation of NeutroAxioms rather than relying on arbitrary assignments. The theoretical
results are verified through an illustration in dynamic threat evaluation. We conclude by posing open problems
regarding the existence of NeutroIdentity and NeutroInverse elements under the defined operation.

DOI 10.5281/zenodo.21440644