context: It is almost certain that John put down the apple. It is unlikely that Julius is a frog. We believe that Brian is yellow. Chances are slight that if 'Julius is a frog and John put down the apple' then Winona is a wolf. It is highly likely that if 'Brian is yellow' or 'Julius is a frog' or both then Bernhard is a lion. It is improbable that if 'Julius is a frog' or 'Brian is yellow' or both then Mary took the milk.
hypothesis: There is little chance that either 'Mary took the milk' or 'Winona is a wolf' but not both.
valid_hypothesis: There is little chance that either 'Mary took the milk' or 'Winona is a wolf' but not both.
invalid_hypothesis: We believe that either 'Mary took the milk' or 'Winona is a wolf' 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
    0.95::factA.
    0.2::factB.
    0.75::factC.
    %hop1
    0.1::factX:-and(factB,factA).
    0.9::factY:-or(factC,factB).
    0.1::factZ:-or(factB,factC).
  
    %hop2
    conclusion:-xor(factZ,factX).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Mary took the milk' or 'Winona is a wolf' but not both.