Propositional Interpretation. (1) There is another possible mode of interpreting the Algebra of Symbolic Logic which forms another application of the calculus to Logic.

Let any letter of the calculus represent a proposition or complex of propositions. The propositions represented are to be either simple categorical propositions, or complexes of such propositions of one or other of two types. One type is the complex proposition which asserts two or more simple propositions to be conjointly true; such a proposition asserts the truth of all its simple components, and the proposer is prepared to maintain any one of them. The verbal form by which such propositions are coupled together is a mere accident: the essential point to be noticed is that the complex proposition is conceived as the product of a set of simple propositions, marked off from all other propositions, and set before the mind by some device, linguistic or otherwise, in such fashion that each single proposition of the set is stated as valid. Hence if one single proposition of the set be disproved, the complex proposition is disproved. Let such a complex of propositions be called a conjunctive complex.

(2) The other type of complex proposition is that which asserts that one at least out of a group of simple propositions, somehow set before the mind, is true. Here again the linguistic device is immaterial, the essential point is that the group of propositions is set before the mind with the understood assertion that one at least is true.