Chances are slight that Lily is white. There is a better than even chance that Mary discarded the milk. It is probable that Greg is a swan. It is probable that if 'Lily is white and Greg is a swan' then Julius is yellow. It is highly likely that if 'Lily is white' or 'Mary discarded the milk' or both then Bernhard is a rhino. There is almost no chance that if 'Mary discarded the milk' or 'Greg is a swan' or both then Sandra left the football.
It is highly unlikely that either 'Sandra left the football' or 'Greg is a swan' but not both.
It is probable that either 'Sandra left the football' or 'Greg is a swan' but not both.
It is highly unlikely that either 'Sandra left the football' or 'Greg is a swan' 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
  0.1::factA.
  0.6::factB.
  0.7::factC.
  %hop1
  0.7::factX:-and(factA,factC).
  0.9::factY:-or(factA,factB).
  0.02::factZ:-or(factB,factC).

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

  query(conclusion).
  
Either 'Sandra left the football' or 'Greg is a swan' but not both.