Graded Symbolic Verification with a Fuzzy Dolev-Yao Attacker Model

Classical symbolic protocol verification under Dolev--Yao uses binary attacker knowledge (known/unknown). This abstraction misses cumulative side-channel settings, where repeated noisy observations progressively improve attacker knowledge. We model this process with a graded attacker view $\mu_K\in[0,1]$, product T-norm leak updates, and finite-grid explicit-state execution in Modified Murphi. The method is optimised with exact concept-lattice attribute reducts and exposes threshold-driven safe-to-fail transitions that are not represented in corresponding binary runs under the same bounded assumptions. Executed results on symmetric and asymmetric protocols, including Needham--Schroeder--Lowe (NSL), show that baseline models passing under crisp semantics can fail once cumulative side-channel leakage is enabled.