Represent Boolean Functions with Linear Classification

Linear classification for logical functions

Imagine using a simple linear classifier to learn from training data whether it’s governed by a boolean logic function or not. That’s a natural and useful thing to do for scientists who want to find causal links or correlations between some observations and others. For example, is there more malaria when it rains AND it is hotter than 35 degrees? Or is there more malaria when either (OR) of these conditions are true?

Let’s look at the following plot, showing the two inputs $A$ and $B$ as coordinates on a graph. The plot shows that only when both are true (with a value of $1$) is the output (shown as green) also true. (False outputs are shown red.)