Symbiotic Autonomous Systems (SAS) are advanced intelligent and cognitive systems exhibiting autonomous collective intelligence enabled by coherent symbiosis of human-machine interactions in hybrid societies. Basic research in the emerging field of SAS has triggered advanced general AI technologies functioning without human intervention or hybrid symbiotic systems synergizing humans and intelligent machines into coherent cognitive systems. This work presents a theoretical framework of SAS underpinned by the latest advances in intelligence, cognition, computer, and system sciences. SAS are characterized by the composition of autonomous and symbiotic systems that adopt bio-brain-social-inspired and heterogeneously synergized structures and autonomous behaviors. This paper explores their cognitive and mathematical foundations. The challenge to seamless human-machine interactions in a hybrid environment is addressed. SAS-based collective intelligence is explored in order to augment human capability by autonomous machine intelligence towards the next generation of general AI, autonomous computers, and trustworthy mission-critical intelligent systems. Emerging paradigms and engineering applications of SAS are elaborated via an autonomous knowledge learning system that symbiotically works between humans and cognitive robots.
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