There is little chance that John discarded the apple. We doubt that Gertrude is a sheep. It is unlikely that Brian is white. It is almost certain that if 'John discarded the apple' or 'Brian is white' or both then Bernhard is a swan. Chances are about even that if either 'Brian is white' or 'Gertrude is a sheep' but not both then Sandra got the milk. It is highly likely that if 'Gertrude is a sheep' or 'John discarded the apple' or both then Greg is gray.
We doubt that either 'Sandra got the milk' or 'Gertrude is a sheep' but not both.
We doubt that either 'Sandra got the milk' or 'Gertrude is a sheep' but not both.
We believe that either 'Sandra got the milk' or 'Gertrude is a sheep' 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
  0.1::factA.
  0.2::factB.
  0.2::factC.
  %hop1
  0.95::factX:-or(factA,factC).
  0.5::factY:-xor(factC,factB).
  0.9::factZ:-or(factB,factA).

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

  query(conclusion).
  
Either 'Sandra got the milk' or 'Gertrude is a sheep' but not both.