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A Smart City is one that makes better use of city data to make our communities better places to live. Typically, this has 3 components: sensing (data collection), analysis and actuation. Privacy, particularly as it relates to citizen's data, is a cross-cutting theme. A Digital Twin (DT) is a virtual replica of a real-world physical entity. Cognitive Digital Twins (CDT) are DTs enhanced with cognitive AI capabilities. Both DTs and CDTs have seen adoption in the manufacturing and industrial sectors however cities are slow to adopt these because of privacy concerns. This work attempts to address these concerns by proposing a Privacy Preserving Federated Learning (PPFL) based Cognitive Digital Twin framework for Smart Cities.