Cloud Manufacturing (CMfg) conceptualizes production assets as virtualized services spanning the full product life cycle, yet existing work largely emphasizes infrastructure and orchestration without formal semantics or closed-form performance models. This paper develops a compact theoretical framework for Cognitive Cloud Manufacturing, expressed through mathematical abstractions independent of implementation. Physical assets are modeled as function-oriented digital twins with typed interfaces, tunable parameters, and symbolic profiles for processing time, throughput, energy consumption, and carbon footprint (PCF). Resources are represented as digital twins offering typed services within a directed acyclic graphs (DAGs) with probabilistic rework. Thus enables additive and analyzable measures of expected makespan, unit energy, and PCF. Cognitive extensions advance digital twins through uncertainty modeling and dynamic belief revision mechanism. It establishes a monotonic property to enhance beliefs directly and improve the expected cost function. Accordingly, we introduce the Cognitive Twin-Aware Earliest-Finish-Time (C-TAEFT) scheduling framework to evaluate task–resource assignments according to weighted priorities of time, energy, and PCF. Formal analysis highlights balance trade-offs, and conceptual case demonstrations , emphasizing the expected responsiveness of scheduling to priority parameters. The framework delivers concise mathematical evaluation, structural proofs, and a minimal analytic basis for evaluating sustainability -aware CMfg systems uncertainty and resource diversity.