It is probably the case that Gertrude is a mouse. Chances are about even that John left the apple. It is almost certain that Brian is a frog. We believe that if either 'Brian is a frog' or 'John left the apple' but not both then Julius is white. It is highly likely that if 'Brian is a frog and Gertrude is a mouse' then Bernhard is gray. There is a better than even chance that if 'John left the apple' or 'Gertrude is a mouse' or both then Lily is a swan.
Chances are about even that either 'John left the apple' or 'Bernhard is gray' but not both.
Chances are about even that either 'John left the apple' or 'Bernhard is gray' but not both.
It is highly unlikely that either 'John left the apple' or 'Bernhard is gray' 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
  0.7::factA.
  0.5::factB.
  0.95::factC.
  %hop1
  0.75::factX:-xor(factC,factB).
  0.9::factY:-and(factC,factA).
  0.6::factZ:-or(factB,factA).

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

  query(conclusion).
  
Either 'John left the apple' or 'Bernhard is gray' but not both.