We believe that John went to the hallway. There is almost no chance that Greg is a swan. We believe that Mary left the football. It is impossible that if 'Mary left the football' or 'John went to the hallway' or both then Julius is a frog. It is probable that if 'Mary left the football' or 'Greg is a swan' or both then Brian is white. It is highly likely that if 'Greg is a swan' or 'Mary left the football' or both then Lily is green.
It is impossible that either 'Lily is green' or 'Julius is a frog' but not both.
It is probable that either 'Lily is green' or 'Julius is a frog' but not both.
It is impossible that either 'Lily is green' or 'Julius is a frog' 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
  0.75::factA.
  0.02::factB.
  0.75::factC.
  %hop1
  0.0::factX:-or(factC,factA).
  0.7::factY:-or(factC,factB).
  0.9::factZ:-or(factB,factC).

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

  query(conclusion).
  
Either 'Lily is green' or 'Julius is a frog' but not both.