context: Chances are about even that Sandra took the football. It is highly likely that Gertrude is a mouse. It is probably not the case that Julius is gray. It is unlikely that if 'Julius is gray' or 'Sandra took the football' or both then Sumit is bored. There is a better than even chance that if either 'Julius is gray' or 'Gertrude is a mouse' but not both then John went to the bedroom. There is little chance that if either 'Julius is gray' or 'Sandra took the football' but not both then Lily is a lion.
hypothesis: It is impossible that either 'Sandra took the football' or 'Lily is a lion' but not both.
valid_hypothesis: Chances are about even that either 'Sandra took the football' or 'Lily is a lion' but not both.
invalid_hypothesis: It is impossible that either 'Sandra took the football' or 'Lily 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
    0.5::factA.
    0.9::factB.
    0.25::factC.
    %hop1
    0.2::factX:-or(factC,factA).
    0.6::factY:-xor(factC,factB).
    0.1::factZ:-xor(factC,factA).
  
    %hop2
    conclusion:-xor(factA,factZ).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Sandra took the football' or 'Lily is a lion' but not both.