context: It is likely that Gertrude is a cat. There is almost no chance that Lily is a frog. We believe that Daniel dropped the apple. Chances are about even that if 'Gertrude is a cat' or 'Lily is a frog' or both then Julius is a lion. It is improbable that if 'Lily is a frog' or 'Daniel dropped the apple' or both then Mary left the milk. It is unlikely that if 'Daniel dropped the apple and Lily is a frog' then Greg is green.
hypothesis: There is little chance that either 'Greg is green' or 'Mary left the milk' but not both.
valid_hypothesis: There is little chance that either 'Greg is green' or 'Mary left the milk' but not both.
invalid_hypothesis: It is almost certain that either 'Greg is green' or 'Mary left the milk' 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.
    0.02::factB.
    0.75::factC.
    %hop1
    0.5::factX:-or(factA,factB).
    0.1::factY:-or(factB,factC).
    0.2::factZ:-and(factC,factB).
  
    %hop2
    conclusion:-xor(factZ,factY).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Greg is green' or 'Mary left the milk' but not both.