Michael Data

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:

$$ P(x,y) \propto 
\begin{cases}
                                   0 & \text{if $\exists x_i$ true and $\exists y_j$ true} \\
                                   1 & \text{otherwise} 
\end{cases}
$$

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