# Michael's Wiki

Given opposing logical consequents $X$ and $Y$ with corresponding antecedents $x_1…x_n$ and $y_1…y_n$, the Two Islands Model models the probability of $X$ or $Y$ being true.

Via Scan Order in Gibbs Sampling: $$P(x,y) \propto \begin{cases}  0 & \text{if \exists x_i true and \exists y_j true} \\ 1 & \text{otherwise}  \end{cases}$$

$$\exists xi \Rightarrow X \& \neg Y \& \nexists y_j$$