context: Chances are about even that Julius is white. Chances are about even that Brian is a rhino. It is certain that Lily is a lion. There is almost no chance that if 'Julius is white and Brian is a rhino' then Jeff left the apple. Chances are about even that if either 'Lily is a lion' or 'Julius is white' but not both then Mary went to the kitchen. Chances are slight that if 'Lily is a lion and Julius is white' then Bernhard is a swan.
hypothesis: We believe that either 'Mary went to the kitchen' or 'Lily is a lion' but not both.
valid_hypothesis: We believe that either 'Mary went to the kitchen' or 'Lily is a lion' but not both.
invalid_hypothesis: We doubt that either 'Mary went to the kitchen' 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.
    0.5::factB.
    1.0::factC.
    %hop1
    0.02::factX:-and(factA,factB).
    0.5::factY:-xor(factC,factA).
    0.1::factZ:-and(factC,factA).
  
    %hop2
    conclusion:-xor(factY,factC).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Mary went to the kitchen' or 'Lily is a lion' but not both.