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A model of an intentional self-observing system is proposed based on the structure and functions of astrocyte-synapse interactions in tripartite synapses. Astrocyte-synapse interactions are cyclically organized and operate via feedforward and feedback mechanisms, formally described by proemial counting. Synaptic, extrasynaptic and astrocyte receptors are interpreted as places with the same or different quality of information processing described by the combinatorics of tritograms. It is hypothesized that receptors on the astrocytic membrane may embody intentional programs that select corresponding synaptic and extrasynaptic receptors for the formation of receptor-receptor complexes. Basically, the act of self-observation is generated if the actual environmental information is appropriate to the intended observation processed by receptor-receptor complexes. This mechanism is implemented for a robot brain enabling the robot to experience environmental information as “its own”. It is suggested that this mechanism enables the robot to generate matches and mismatches between intended observations and the observations in the environment, based on the cyclic organization of the mechanism. In exploring an unknown environment the robot may stepwise construct an observation space, stored in memory, commanded and controlled by the intentional self-observing system. Finally, the role of self-observation in machine consciousness is shortly discussed.