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To propose a mathematical model of consciousness and will, we first simulatedthe inverted qualia with a toy model of a neural network. As a result, weconfirmed that there can be an inverted qualia on the neural network. In otherwords, the qualia were individual-dependent and considered difficult as anindicator of consciousness and will. To solve that difficulty, we introduce aprobability space and a random variable into a set of qualia and define apublic language for events. Based on this idea of public language,consciousness and will are modeled. In this proposal, future actions arerandomly selected from the comparison between "recognition of events" byexternal observation and past episodic memory, and the actual "recognition ofactions" is regarded as the occurrence of consciousness. The basic formula isalso derived. This proposal is compared with other past philosophicaldiscussions.

Mathematical definition of public language, and modeling of will and consciousness based on the public language