It is probably the case that John discarded the apple. It is probably the case that Mary dropped the milk. We doubt that Brian is a lion. It is unlikely that if 'John discarded the apple' or 'Mary dropped the milk' or both then Daniel put down the milk. It is certain that if either 'Brian is a lion' or 'John discarded the apple' but not both then Lily is white. There is almost no chance that if either 'Brian is a lion' or 'John discarded the apple' but not both then Bill left the football.
There is little chance that either 'Mary dropped the milk' or 'Brian is a lion' but not both.
There is a better than even chance that either 'Mary dropped the milk' or 'Brian is a lion' but not both.
There is little chance that either 'Mary dropped the milk' or 'Brian is a lion' 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
  0.7::factA.
  0.7::factB.
  0.2::factC.
  %hop1
  0.2::factX:-or(factA,factB).
  1.0::factY:-xor(factC,factA).
  0.02::factZ:-xor(factC,factA).

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

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