It is highly unlikely that Bernhard is a frog. Chances are about even that Gertrude is a cat. There is almost no chance that Julius is gray. It is unlikely that if 'Gertrude is a cat' or 'Julius is gray' or both then Mary went to the office. It is highly unlikely that if 'Julius is gray and Gertrude is a cat' then Lily is a swan. There is a better than even chance that if 'Julius is gray' or 'Gertrude is a cat' or both then Bill left the milk.
It is certain that either 'Bill left the milk' or 'Lily is a swan' but not both.
It is probably not the case that either 'Bill left the milk' or 'Lily is a swan' but not both.
It is certain that either 'Bill left the milk' or 'Lily 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
  0.05::factA.
  0.5::factB.
  0.02::factC.
  %hop1
  0.2::factX:-or(factB,factC).
  0.05::factY:-and(factC,factB).
  0.6::factZ:-or(factC,factB).

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

  query(conclusion).
  
Either 'Bill left the milk' or 'Lily is a swan' but not both.