context: We doubt that Lily is a lion. It is almost certain that Bernhard is white. There is almost no chance that Jeff left the apple. Chances are about even that if either 'Jeff left the apple' or 'Lily is a lion' but not both then Greg is a rhino. It is highly likely that if either 'Jeff left the apple' or 'Lily is a lion' but not both then John took the milk. We believe that if 'Jeff left the apple' or 'Lily is a lion' or both then Mary got the football.
hypothesis: It is probable that either 'Lily is a lion' or 'Mary got the football' but not both.
valid_hypothesis: It is highly unlikely that either 'Lily is a lion' or 'Mary got the football' but not both.
invalid_hypothesis: It is probable that either 'Lily is a lion' or 'Mary got the football' 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
    0.2::factA.
    0.95::factB.
    0.02::factC.
    %hop1
    0.5::factX:-xor(factC,factA).
    0.9::factY:-xor(factC,factA).
    0.75::factZ:-or(factC,factA).
  
    %hop2
    conclusion:-xor(factA,factZ).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Lily is a lion' or 'Mary got the football' but not both.