context: It is probably the case that Brian is white. There is almost no chance that Gertrude is a cat. It is probably not the case that Sandra got the milk. We believe that if either 'Brian is white' or 'Gertrude is a cat' but not both then Lily is green. It is highly unlikely that if 'Brian is white' or 'Gertrude is a cat' or both then Bernhard is a frog. It is impossible that if 'Sandra got the milk and Gertrude is a cat' then Mary went to the bedroom.
hypothesis: It is impossible that 'Sandra got the milk and Gertrude is a cat'.
valid_hypothesis: It is impossible that 'Sandra got the milk and Gertrude is a cat'.
invalid_hypothesis: It is certain that 'Sandra got the milk and Gertrude is a cat'.
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.
    0.25::factC.
    %hop1
    0.75::factX:-xor(factA,factB).
    0.05::factY:-or(factA,factB).
    0.0::factZ:-and(factC,factB).
  
    %hop2
    conclusion:-and(factC,factB).
  
    query(conclusion).
    
hypothesis_assertion: 'Sandra got the milk and Gertrude is a cat'.