The rapid integration of artificial intelligence (AI) into public governance systems has profoundly impacted how government agencies make administrative decisions, develop policies and deliver services in the context of democratic organizations. However, existing governance theories are unable to articulate how human cognition and machine intelligence cooperate in a co-decision making environment within government. A pervasive problem in existing governance literature and theories about AI and government is the lack of clarity or the fragmentation of theory regarding the interaction between human intelligence and machine intelligence in such hybrid governance systems particularly when concerning the accountability, the legitimacy, and the quality of decisions in an AI public administration setting. This study attempts to bridge this void. More specifically, this study proposes Cognitive Governance Systems (CGS) Theory as an original explanatory framework of the interaction between human intelligence and machine intelligence in a co-decision making context of democratic government. The research follows a theory building and theory validation-oriented design that is achieved via systematic literature review synthesis. Within this new CGS Theory, we present a cognitive system-based view of governance, conceptualized as a distributed cognition system that includes six elements: human intelligence, machine intelligence, human and machine learning cognition, the interface among those two intelligences (interaction mechanism), the framework on which governance is situated (democratic principles), and the capability of that governance system to perform, respond and evolve (resilience and adaptiveness). This new paradigm in cognitive governance theory explains why the interplay among these six elements influences the quality of decision making, the effectiveness of public policies, and the sustainability of public trust in the age of AI enabled governance systems. Our approach is built with a view to enable future empirical testing, with mixed-method techniques, such as the Delphi study method, survey instruments, and structural equation modeling (SEM).