context: There is a very good chance that Mary took the milk. It is highly unlikely that Bernhard is a swan. We doubt that Julius is white. It is certain that if either 'Julius is white' or 'Mary took the milk' but not both then Jessica is a cat. It is highly unlikely that if 'Bernhard is a swan and Mary took the milk' then Fred went to the garden. There is almost no chance that if 'Julius is white' or 'Bernhard is a swan' or both then Sandra dropped the apple.
hypothesis: We believe that either 'Julius is white' or 'Sandra dropped the apple' but not both.
valid_hypothesis: We doubt that either 'Julius is white' or 'Sandra dropped the apple' but not both.
invalid_hypothesis: We believe that either 'Julius is white' or 'Sandra dropped the apple' but not both.
problog: 
    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
    0.8::factA.
    0.05::factB.
    0.2::factC.
    %hop1
    1.0::factX:-xor(factC,factA).
    0.05::factY:-and(factB,factA).
    0.02::factZ:-or(factC,factB).
  
    %hop2
    conclusion:-xor(factC,factZ).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Julius is white' or 'Sandra dropped the apple' but not both.