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===Special classes of propositions===
===Special classes of propositions===
A ''basic proposition'', ''coordinate proposition'', or ''simple proposition'' in the universe of discourse <math>[a_1, \ldots, a_n]</math> is one of the propositions in the set <math>\{ a_1, \ldots, a_n \}.</math>
Among the <math>2^{2^n}</math> propositions in <math>[a_1, \ldots, a_n]</math> are several families of <math>2^n\!</math> propositions each that take on special forms with respect to the basis <math>\{ a_1, \ldots, a_n \}.</math> Three of these families are especially prominent in the present context, the ''linear'', the ''positive'', and the ''singular'' propositions. Each family is naturally parameterized by the coordinate <math>n\!</math>-tuples in <math>\mathbb{B}^n</math> and falls into <math>n + 1\!</math> ranks, with a binomial coefficient <math>\tbinom{n}{k}</math> giving the number of propositions that have rank or weight <math>k.\!</math>
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