There is almost no chance that Greg is gray. It is highly likely that John took the apple. It is probably not the case that Lily is a swan. There is a very good chance that if either 'John took the apple' or 'Greg is gray' but not both then Winona is a wolf. Chances are about even that if 'Greg is gray and John took the apple' then Bernhard is a frog. It is probable that if 'Lily is a swan and Greg is gray' then Mary got the milk.
We doubt that either 'Lily is a swan' or 'John took the apple' but not both.
It is likely that either 'Lily is a swan' or 'John took the apple' but not both.
We doubt that either 'Lily is a swan' or 'John 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
  0.02::factA.
  0.9::factB.
  0.25::factC.
  %hop1
  0.8::factX:-xor(factB,factA).
  0.5::factY:-and(factA,factB).
  0.7::factZ:-and(factC,factA).

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

  query(conclusion).
  
Either 'Lily is a swan' or 'John took the apple' but not both.