It is certain that Greg is white. It is likely that Gertrude is a cat. We doubt that Mary dropped the apple. It is probably not the case that if 'Gertrude is a cat' or 'Greg is white' or both then Emily is a wolf. There is almost no chance that if 'Greg is white' or 'Mary dropped the apple' or both then Julius is a lion. Chances are about even that if either 'Gertrude is a cat' or 'Greg is white' but not both then Brian is yellow.
It is unlikely that either 'Julius is a lion' or 'Mary dropped the apple' but not both.
It is unlikely that either 'Julius is a lion' or 'Mary dropped the apple' but not both.
There is a very good chance that either 'Julius is a lion' or 'Mary dropped the apple' but not both.

  and(A,B) :- A,B.
  or(A,B) :- A;B.
  nand(A,B) :- not(and(A,B)).
  nor(A,B) :- not(or(A,B)).
  xor(A,B) :- or(A,B), nand(A,B).

  %hop0
  1.0::factA.
  0.7::factB.
  0.2::factC.
  %hop1
  0.25::factX:-or(factB,factA).
  0.02::factY:-or(factA,factC).
  0.5::factZ:-xor(factB,factA).

  %hop2
  conclusion:-xor(factY,factC).

  query(conclusion).
  
Either 'Julius is a lion' or 'Mary dropped the apple' but not both.