Limits of pl Example The previous example can be abstracted further like O P: All As have property b @ Q: C is one of As Remark o There is no relation between P and Q o The flaw is that"is/in"relationship can not be expressed by Pl O Consider there exists .. " ,"all among and"ony…." A richer language is neededLimits of PL Example The previous example can be abstracted further like 1 P: All As have property B. 2 Q: C is one of As. Remark 1 There is no relation between P and Q. 2 The flaw is that ”is/in” relationship can not be expressed by PL. 3 Consider ”there exists ...”, ”all ...”, ”among ...”, and ”only ...”. 4 A richer language is needed. Yi Li (Fudan University) Discrete Mathematics May 9, 2012 11 / 22