It is highly unlikely that Julius is gray. It is highly likely that Mary got the football. Chances are slight that Daniel left the milk. It is certain that if either 'Mary got the football' or 'Julius is gray' but not both then Sandra took the apple. It is unlikely that if 'Julius is gray' or 'Mary got the football' or both then Bernhard is white. It is probably not the case that if 'Mary got the football' or 'Daniel left the milk' or both then Lily is green.
It is unlikely that either 'Julius is gray' or 'Sandra took the apple' but not both.
It is highly likely that either 'Julius is gray' or 'Sandra took the apple' but not both.
It is unlikely that either 'Julius is gray' or 'Sandra took 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
  0.05::factA.
  0.9::factB.
  0.1::factC.
  %hop1
  1.0::factX:-xor(factB,factA).
  0.2::factY:-or(factA,factB).
  0.25::factZ:-or(factB,factC).

  %hop2
  conclusion:-xor(factA,factX).

  query(conclusion).
  
Either 'Julius is gray' or 'Sandra took the apple' but not both.