The idea of using information-theoretical concepts to quantify the notion of explanatory power of theories is an attractive one. Where the theory is adequately represented by a probability measure p on Boolean algebra A of propositions, it is natural to think of measuring explanatory power by some function of H(A), the entropy or uncertainty of p. But recently, Greeno and others have been exploring measures of explanatory power which are suggested by more detailed representations of theories - representations which are themselves suggested by communication-theoretical analogies.

To avoid inessential complications, suppose that the Boolean algebra A is finite, and let ‘a’ range over the atoms of A, viz., the strongest propositions in A which are not logically false. (Any two atoms are logically incompatible, and any proposition in A is expressible as a disjunction of atoms.) Then we have

where we set p(a) logp(a)=0 in case p(a)=0.