It is probable that Julius is white. We believe that Mary got the football. It is certain that Daniel took the apple. It is highly unlikely that if either 'Mary got the football' or 'Daniel took the apple' but not both then Jeff went to the garden. There is a very good chance that if either 'Julius is white' or 'Daniel took the apple' but not both then Bill left the milk. We doubt that if 'Daniel took the apple' or 'Mary got the football' or both then Gertrude is a mouse.
There is a better than even chance that either 'Mary got the football' or 'Bill left the milk' but not both.
There is a better than even chance that either 'Mary got the football' or 'Bill left the milk' but not both.
There is little chance that either 'Mary got the football' or 'Bill left the milk' 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.
  0.75::factB.
  1.0::factC.
  %hop1
  0.05::factX:-xor(factB,factC).
  0.8::factY:-xor(factA,factC).
  0.2::factZ:-or(factC,factB).

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

  query(conclusion).
  
Either 'Mary got the football' or 'Bill left the milk' but not both.