Brachman and Levesque, chapter 2 exercise 4 . Formulate the requirements below as sentences of first order logic and show Summary: Brachman and Levesque, chapter 2 exercise 4 . Question . Formulate the requirements below as sentences of first order logic and show that the two of them cannot be true together in any interpretation. (This is the barber's paradox by Bertrand Russell.) 1. Anyone who does not shave himself must be shaved by the barber [note the barber - some unique person, not a barber]. 2. Whomever the barber shaves, must not shave himself. Hints: introduce a constant for the barber and a binary predicate Shaves(x, y). Answer . Translation: 1. x(ŽShaves(x, x) Shaves(barber, x)) 2. x(Shaves(barber, x) ŽShaves(x, x)) Suppose some interpretation (D, I) satisfies both 1 and 2. There is an object in D which is the meaning of `barber' in that interpretation, I(barber). Let us call it b. This b either shaves himself or not, or in logic speak the pair (b, b) is either in the interpretation I(Shaves) of the predicate Shaves, or not. First suppose it is: (b, b) I(Shaves). Then since the second sentence is true in (D, I), for every assignment v: (D, I), v |= Shaves(barber, x) ŽShaves(x, x) Collections: Computer Technologies and Information Sciences