It is unlikely that Mary dropped the milk. It is impossible that Lily is a lion. We doubt that Winona is a mouse. It is probably not the case that if either 'Winona is a mouse' or 'Mary dropped the milk' but not both then John discarded the apple. It is likely that if 'Mary dropped the milk and Lily is a lion' then Greg is white. It is certain that if 'Lily is a lion' or 'Mary dropped the milk' or both then Julius is gray.
It is certain that either 'Lily is a lion' or 'Winona is a mouse' but not both.
We doubt that either 'Lily is a lion' or 'Winona is a mouse' but not both.
It is certain that either 'Lily is a lion' or 'Winona is a mouse' 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
  0.2::factA.
  0.0::factB.
  0.2::factC.
  %hop1
  0.25::factX:-xor(factC,factA).
  0.7::factY:-and(factA,factB).
  1.0::factZ:-or(factB,factA).

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

  query(conclusion).
  
Either 'Lily is a lion' or 'Winona is a mouse' but not both.