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

To propose a mathematical model of consciousness and will, we first simulated the inverted qualia with a toy model of a neural network. As a result, we confirmed that there can be an inverted qualia on the neural network. In other words, the qualia were individual-dependent and considered difficult as an indicator of consciousness and will. To solve that difficulty, we introduce a probability space and a random variable into a set of qualia and define a public language for events. Based on this idea of public language, consciousness and will are modeled. In this proposal, future actions are randomly selected from the comparison between "recognition of events" by external observation and past episodic memory, and the actual "recognition of actions" is regarded as the occurrence of consciousness. The basic formula is also derived. This proposal is compared with other past philosophical discussions.