There is almost no chance that Lily is a frog. It is unlikely that Julius is yellow. There is almost no chance that Mary left the apple. It is highly unlikely that if either 'Mary left the apple' or 'Lily is a frog' but not both then Brian is white. Chances are about even that if 'Julius is yellow and Lily is a frog' then Greg is green. There is a very good chance that if 'Mary left the apple' or 'Julius is yellow' or both then Bernhard is a lion.
We doubt that either 'Bernhard is a lion' or 'Brian is white' but not both.
We doubt that either 'Bernhard is a lion' or 'Brian is white' but not both.
It is highly likely that either 'Bernhard is a lion' or 'Brian is white' 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
  0.02::factA.
  0.2::factB.
  0.02::factC.
  %hop1
  0.05::factX:-xor(factC,factA).
  0.5::factY:-and(factB,factA).
  0.8::factZ:-or(factC,factB).

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

  query(conclusion).
  
Either 'Bernhard is a lion' or 'Brian is white' but not both.