context: It is impossible that Brian is yellow. It is certain that John dropped the milk. There is a very good chance that Winona is a sheep. There is almost no chance that if 'Brian is yellow and John dropped the milk' then Jeff left the apple. It is highly likely that if 'Winona is a sheep and Brian is yellow' then Greg is a swan. There is a very good chance that if 'Winona is a sheep and Brian is yellow' then Bernhard is a frog.
hypothesis: It is certain that either 'John dropped the milk' or 'Bernhard is a frog' but not both.
valid_hypothesis: It is certain that either 'John dropped the milk' or 'Bernhard is a frog' but not both.
invalid_hypothesis: We doubt that either 'John dropped the milk' or 'Bernhard is a frog' 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
    0.0::factA.
    1.0::factB.
    0.8::factC.
    %hop1
    0.02::factX:-and(factA,factB).
    0.9::factY:-and(factC,factA).
    0.8::factZ:-and(factC,factA).
  
    %hop2
    conclusion:-xor(factB,factZ).
  
    query(conclusion).
    
hypothesis_assertion: Either 'John dropped the milk' or 'Bernhard is a frog' but not both.