It is unlikely that Bill went to the kitchen. Chances are slight that Julius is gray. It is certain that Gertrude is a sheep. It is likely that if either 'Gertrude is a sheep' or 'Julius is gray' but not both then Greg is gray. It is impossible that if either 'Gertrude is a sheep' or 'Bill went to the kitchen' but not both then Brian is a lion. It is almost certain that if 'Bill went to the kitchen and Gertrude is a sheep' then Mary grabbed the milk.
We believe that either 'Brian is a lion' or 'Bill went to the kitchen' but not both.
We doubt that either 'Brian is a lion' or 'Bill went to the kitchen' but not both.
We believe that either 'Brian is a lion' or 'Bill went to the kitchen' 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.
  0.1::factB.
  1.0::factC.
  %hop1
  0.7::factX:-xor(factC,factB).
  0.0::factY:-xor(factC,factA).
  0.95::factZ:-and(factA,factC).

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

  query(conclusion).
  
Either 'Brian is a lion' or 'Bill went to the kitchen' but not both.