 Burger and Heidema 1994 compare theories by positive and negative sentences. A positive sentence is one that can be constructed out of \(\amp,\) \(\vee\) and any true basic sentence. A negative sentence is one that can be constructed out of \(\amp,\) \(\vee\) and any false basic sentence. Call a sentence pure if it is either positive or negative. If we take the relevance criterion to be purity, and combine that with the relevant consequence schema above, we have Burger and Heidema’s proposal, which yields a reasonable set of intuitive judgments. Unfortunately purity (like atomicity) does not quite satisfy the constraint that \(A\) be equivalent to the class of its relevant consequences. For example, if \(h\) and \(r\) are both true then \(({\sim}h\vee r)\) and \((h\vee{\sim}r)\) both have the same pure consequences (namely, none).