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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} $$

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