 SOD refers to the fact philosophical accounts of information are yet to give an account of the informativeness of logical truths and deductive inferences. Bar-Hillel and Carnap’s theory of semantic information assigns minimal information to logical truths (and valid deductive inferences can be transformed into logical truths by conjoining the premises into an antecedent of a conditional that takes the conclusion as its consequent). Where \(\top\) is an arbitrary tautology, given that \(\top\) will be false in all possible worlds, we have the following via  (1),  (2), and  (3)  respectively: