  Boole turned to the topic of the interpretability of a logical function in Chapter VI Section 13.  He had already stated in MAL that every equation is interpretable (by showing an equation was equivalent to a collection of constituent equations). However algebraic terms need not be interpretable, e.g., \(1+1\) is not interpretable. Some terms are partially interpretable, and equivalent terms can have distinct domains of interpretability.   In Chapter VI  Section 13, he comes to the conclusion that the condition for a polynomial \(p\) to be equivalent to a (totally) interpretable function is that it satisfy \(p^2 = p\), in which case it is equivalent to a sum of distinct constituents, namely those belonging to the non-vanishing modulii of \(p\). A polynomial is idempotent if and only if all of its modulii are idempotent, that is, they are in \(\{0, 1\}\), in which case the expansion of the polynomial is a sum of distinct constituents (or it is 0).