context: It is probable that Lily is a frog. It is likely that Gertrude is a mouse. It is highly likely that Emily is a wolf. We doubt that if 'Gertrude is a mouse and Emily is a wolf' then Julius is white. It is unlikely that if 'Gertrude is a mouse' or 'Emily is a wolf' or both then John put down the milk. It is probably the case that if either 'Lily is a frog' or 'Gertrude is a mouse' but not both then Bernhard is gray.
hypothesis: There is almost no chance that 'John put down the milk and Julius is white'.
valid_hypothesis: There is almost no chance that 'John put down the milk and Julius is white'.
invalid_hypothesis: It is highly likely that 'John put down the milk and Julius is white'.
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.
    0.7::factB.
    0.9::factC.
    %hop1
    0.2::factX:-and(factB,factC).
    0.2::factY:-or(factB,factC).
    0.7::factZ:-xor(factA,factB).
  
    %hop2
    conclusion:-and(factY,factX).
  
    query(conclusion).
    
hypothesis_assertion: 'John put down the milk and Julius is white'.