Quiz 4: Mostly Quantification

!You will be sadly disappointed if you think that these are a substitute for attending class!

Lecture 27: Multiple Quantification (11/29/04) – §11.2-4

• What are the following predicates?
  
• Ex Larger(x, y)
• Ex Larger(y, x)
• Do these say the same thing?
  
• Ex SameRow(x, y)
• Ex SameRow(y,x)
• Do these say the same thing? Why is this case different to the first?
  
• Ax Likes(x, y)
• Ay Likes(x, y)
• Do these say the same thing?

• Sentences with logically complex predicates: what do the following say?
• Ey Ex Larger(x, y)
• Ey Ex Larger(y, x)
• Do these say the same thing?
• Ay Ex Larger(x, y)
• Ay Ex Larger(y, x)
• Do these say the same thing?
• Ay Ax SameRow(x, y)
• Ax Ay SameRow(x, y)
• Do these say the same thing?
• Ey Ax ¬Larger(x, y)
• Ex Ay ¬Larger(x, y)
• Do these say the same thing?

• What do the following say?
• Ay ((Cube(y) ^ SameRow(y, a)) –> Large(y))
• Ay ((Cube(y) ^ Large(y)) –> (SameRow(y, a) ^ SameCol(y, a)))
• Ey (Cube(y) ^ Small(y) ^ Adjoins(y, a))
• EyAx (Cube(y) ^ SameSize(y, x))
• AxEy (Cube(y) ^ SameSize(y, x))
• AxEy((Cube(x) ^ SameRow(a, x)) –> SameSize(x, y))
• EyAx((Cube(x) ^ SameRow(a, x)) –> SameSize(x, y))