context: There is almost no chance that Lily is white. Chances are about even that Bernhard is a swan. Chances are slight that Mary took the milk. There is little chance that if 'Mary took the milk' or 'Bernhard is a swan' or both then Jeff went to the bedroom. There is almost no chance that if 'Mary took the milk' or 'Bernhard is a swan' or both then Brian is a lion. Chances are about even that if 'Lily is white and Bernhard is a swan' then John dropped the milk.
hypothesis: Chances are about even that either 'Mary took the milk' or 'Bernhard is a swan' but not both.
valid_hypothesis: Chances are about even that either 'Mary took the milk' or 'Bernhard is a swan' but not both.
invalid_hypothesis: It is impossible that either 'Mary took the milk' or 'Bernhard is a swan' 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
    0.02::factA.
    0.5::factB.
    0.1::factC.
    %hop1
    0.1::factX:-or(factC,factB).
    0.02::factY:-or(factC,factB).
    0.5::factZ:-and(factA,factB).
  
    %hop2
    conclusion:-xor(factC,factB).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Mary took the milk' or 'Bernhard is a swan' but not both.