  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.
