context: It is highly unlikely that John moved to the office. Chances are slight that Greg is a rhino. There is a better than even chance that Mary left the milk. It is highly likely that if 'Mary left the milk and Greg is a rhino' then Sandra dropped the apple. There is little chance that if 'Mary left the milk and Greg is a rhino' then Lily is yellow. It is highly likely that if 'Mary left the milk and John moved to the office' then Brian is a swan.
hypothesis: It is highly unlikely that either 'Lily is yellow' or 'Sandra dropped the apple' but not both.
valid_hypothesis: It is highly unlikely that either 'Lily is yellow' or 'Sandra dropped the apple' but not both.
invalid_hypothesis: Chances are about even that either 'Lily is yellow' or 'Sandra dropped the apple' 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
    0.05::factA.
    0.1::factB.
    0.6::factC.
    %hop1
    0.9::factX:-and(factC,factB).
    0.1::factY:-and(factC,factB).
    0.9::factZ:-and(factC,factA).
  
    %hop2
    conclusion:-xor(factY,factX).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Lily is yellow' or 'Sandra dropped the apple' but not both.