context: It is unlikely that John grabbed the apple. It is improbable that Brian is a swan. It is likely that Lily is a frog. There is a better than even chance that if either 'Lily is a frog' or 'John grabbed the apple' but not both then Greg is a swan. Chances are about even that if 'Lily is a frog' or 'Brian is a swan' or both then Bernhard is yellow. It is highly likely that if 'Lily is a frog' or 'Brian is a swan' or both then Daniel put down the milk.
hypothesis: It is probably not the case that either 'Lily is a frog' or 'Bernhard is yellow' but not both.
valid_hypothesis: It is probably not the case that either 'Lily is a frog' or 'Bernhard is yellow' but not both.
invalid_hypothesis: It is certain that either 'Lily is a frog' or 'Bernhard is yellow' 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.
    0.1::factB.
    0.7::factC.
    %hop1
    0.6::factX:-xor(factC,factA).
    0.5::factY:-or(factC,factB).
    0.9::factZ:-or(factC,factB).
  
    %hop2
    conclusion:-xor(factC,factY).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Lily is a frog' or 'Bernhard is yellow' but not both.