Formal examination of operators and properties of generalized ambiguous four-degree logic

Abstract

 In this paper, we formally introduce the Generalized Ambiguous Quadruple Degree Membership Logic (GAF-DL) as an extension of the foundational principles of fuzzy logic and neutrosophic logic, incorporating Belnap's four-valued logic to provide a binary structure for truth evaluation. This paper explores a discrete intermediary system of Four-Degree Membership Logic. It presents a formal definition of a standard set of logical operators (Negation, Conjunction, Disjunction, Implication, and Equivalence). It analyzes their key properties, including associative laws, the Law of Contradiction, De Morgan's Laws, distributive laws, and commutative laws. Our study demonstrates that GAF-DL offers a computationally efficient and semantically rich approach for modelling phenomena where truth is not merely partial but also context-dependent and subject to multiple interpretations.