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PHIL12A Section answers, 18 April 2011 Julian Jonker FOL translation exercises 1. Look carefully at how the following sentences have been translated into FOL. (You should try to do them on your own ﬁrst.) (a) Each cube is to the left of a tetrahedron. Actually this is ambiguous. Here is the weak version: x(Cube(x) → ∃ y(Tet(y) LeftOf(x,y))) Here is the strong version: x(Tet(x) ∧ ∀ y(Cube(y) LeftOf(y,x))) (b) No cube to the right of a tetrahedron is to the left of a larger dodecahedron. This is a terrible sentence. It is doubly ambiguous. Is there just one tetrahedron, or could there be many? (I say the latter in my translation.) Is the dodecahedron larger than the tetrahedron, or than the cube (I again say the latter). Don’t mix up the variables in what follows! Exercise: give translations reﬂecting the other possible meanings of the English. x((Cube(x) ∧∃ y(Tet(y) RightOf(x,y))) → ¬∃ y(Dodec(y) Larger(y,x) RightOf(x,y))) (c) If a freshman takes a logic class, he or she is smart. x((Freshman(x)

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