Expressive Power of PL Ramp dle If Socrates is a man then Socrates is mortal Solution(Propositional Logic) O A: Socrates is a man B: Socrates is mortal We can represent the previous statement as A-,B o If A is true, then we know B is true
Expressive Power of PL . Example . .If Socrates is a man then Socrates is mortal. . Solution (Propositional Logic) . . 1. A: ”Socrates is a man”. 2. B: ”Socrates is mortal”. 3. We can represent the previous statement as A → B. 4. If A is true, then we know B is true. Yi Li (Fudan University) Discrete Mathematics May 7, 2013 6 / 20
Limits of pl Xam dle Given two statements: "All men are mortal"and Socrates is a man". What can we do Solution o We all know the following statement holding Socrates is mortal o If they are formalized as two proposition, nothing can be implied
Limits of PL . Example . . Given two statements:”All men are mortal” and ”Socrates is a man”. What can we do? . Solution . . 1. We all know the following statement holding, ”Socrates is mortal”. 2. If they are formalized as two proposition, nothing can be implied. Yi Li (Fudan University) Discrete Mathematics May 7, 2013 7 / 20