In Smullyan's formulation, the overall statement uttered by a liar must be logically false, even though it might contain conjuncts that are true, or might conve

In Smullyan's formulation, the overall statement uttered by a liar must be logically false, even though it might contain conjuncts that are true, or might convey large amounts of useful and accurate information. For example, Smullyan would allow a liar to say "the sky is blue and cats are cute and 1+1=3". I might have phrased that confusingly when I said that they lie about everything in every statement. I should probably have said that they are never allowed to make any statement that they believe is true.