Stochastic, Continuous, and Turing Decidable Propositional Logic

In the current state Propositional logic is a very powerful branch of mathematics; however, it is also limited by the insistence that $p\vee
eg p$, one of the issues is that sometimes $p$ is intrinsically stochastic. The only works that anyhow address this issue are [1-3]. In the first half of the paper I will derive the extension for tautology that includes stochastic propositions (i.e. where there is a probability distribution associated with $p$), formalize the notion of probability distribution of probability distribution, and derive the extension of tautology that includes undecidability and non-existence - $p\oplus
eg p\oplus ?p\oplus!p\oplus
ot\exists p$ (also see [4-7]). In the second half I will apply this new notation to the standard problems of Turing decidablility: I will show that the new notation effectively eliminates the need for words (which is a limiting factor of the current state of decidability theory). Lastly, I will construct a new machine that can solve problems Turing machines can't. This machine is going to be more powerful because it can enter a state of superposition. Lastly, I will show that there will be no need to create a new machine for "superposition of superposition of states."