HOMEWORK #5: F.O.L. REPRESENTATION

1. Provide an FOL syntax and semantics to represent the following English sentences, and then represent them:
   • (a) Not all students take both Computer Science and Philosophy.
   • (b) Only one student failed Computer Science.
   • (c) Only one student failed both Computer Science and Philosophy.
   • (d) The best score in Computer Science was better than the best score in Philosophy.
   • (e) Every person who dislikes all computer scientists is smart.
   • (f) No person likes a smart computer scientist.
   • (g) There is a woman who likes all men who are not computer scientists.
   • (h) There is a barber who shaves all men in town who do not shave themselves.
   • (i) No person likes a professor unless the professor is smart.
   • (j) Politicians can fool some of the people all of the time, and they can fool all of the people some of the time, but they can't fool all of the people all of the time.

2. Do the same for the following sentences, but be warned that they might use connectives in ways that are different from FOL. For each sentence, give an FOL translation that preserves the intended English meaning if you can, as well as a straightforward translation (as if the connectives had their regular FOL meaning).
   • (a) One more outburst like that, and you'll be in contempt of court.
   • (b) There's a good movie on TV tonight, if you're interested.
   • (c) The special this morning is ham and eggs.
   • (d) If I don't jump off the Empire State Building, then, if I jump off the Empire State Building, then I float safely to the ground.
   • (e) If it is not the case that, if you attempt this exercise, then you will get an F, then you will attempt this exercise.
   • (f) If you lived here, then you would be home now. If you were home now, then you would not be here. Therefore, if you lived here, then you would not be here.

   Problem 2 is probably easier to do in propositional logic than in FOL. In most, if not all, of the sentences, the crucial point is that the connectives are odd. But note that propositional logic is, in fact, entirely contained within FOL: As the B&L text points out, a 0-place predicate is just a propositional-logic wff!

   So, for example, for sentence 2(a), you do NOT need to worry about how to represent things like "one more outburst like that" or like "you will be in contempt of court". The issue is really whether that sentence is really a conjunction (as it appears to be on the surface) or something else.