It is unlikely that Julius is gray. It is probable that Greg is a swan. Chances are slight that Mary moved to the garden. It is likely that if either 'Julius is gray' or 'Mary moved to the garden' but not both then Gertrude is a mouse. There is almost no chance that if 'Mary moved to the garden and Greg is a swan' then John took the football. It is improbable that if 'Mary moved to the garden and Julius is gray' then Brian is yellow.
It is unlikely that either 'Gertrude is a mouse' or 'John took the football' but not both.
It is unlikely that either 'Gertrude is a mouse' or 'John took the football' but not both.
There is a very good chance that either 'Gertrude is a mouse' or 'John took the football' 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
  0.2::factA.
  0.7::factB.
  0.1::factC.
  %hop1
  0.7::factX:-xor(factA,factC).
  0.02::factY:-and(factC,factB).
  0.1::factZ:-and(factC,factA).

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

  query(conclusion).
  
Either 'Gertrude is a mouse' or 'John took the football' but not both.