context: It is probably the case that Julius is a lion. We believe that Sandra dropped the milk. Chances are slight that Daniel got the milk. There is little chance that if 'Sandra dropped the milk' or 'Julius is a lion' or both then Lily is a frog. There is almost no chance that if 'Julius is a lion' or 'Sandra dropped the milk' or both then Bernhard is yellow. There is a better than even chance that if either 'Daniel got the milk' or 'Julius is a lion' but not both then Mary went to the kitchen.
hypothesis: We doubt that either 'Bernhard is yellow' or 'Julius is a lion' but not both.
valid_hypothesis: It is probable that either 'Bernhard is yellow' or 'Julius is a lion' but not both.
invalid_hypothesis: We doubt that either 'Bernhard is yellow' or 'Julius is a lion' 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
    0.7::factA.
    0.75::factB.
    0.1::factC.
    %hop1
    0.1::factX:-or(factB,factA).
    0.02::factY:-or(factA,factB).
    0.6::factZ:-xor(factC,factA).
  
    %hop2
    conclusion:-xor(factY,factA).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Bernhard is yellow' or 'Julius is a lion' but not both.