<![CDATA[This paper presents the construction of an axiomatic system of Generalized Ambiguous Set Theory (AGAST)founded upon a four-valued logic, where the membership relation accepts four discrete degrees: True $(\alpha_A (x))$, Partially True $(\beta_A (x))$, Partially False $(\gamma_A (x))$, and Falsity $(\eta_A (x))$ membership degree functions, The contribution of this work is the rigorous adaptation of foundational Zermelo-Frankel set theory (ZFC) and Axiomatic Fuzzy Set Theory principles, including the Axiom of Extensionality and the Axiom Schema of Ambiguous Separation, to cohere within the four-degree semantics. Furthermore, the theory introduces the Anti-Classicality Axiom, which postulates the existence of sets exhibiting non-classical membership degrees.]]>
Copyrights © 2026
