context: It is almost certain that Greg is white. It is improbable that Brian is gray. It is improbable that Julius is a swan. It is highly likely that if 'Julius is a swan' or 'Brian is gray' or both then Mary went to the office. Chances are about even that if 'Julius is a swan and Greg is white' then John took the apple. It is almost certain that if 'Julius is a swan and Greg is white' then Sandra left the milk.
hypothesis: There is little chance that either 'Sandra left the milk' or 'Mary went to the office' but not both.
valid_hypothesis: There is little chance that either 'Sandra left the milk' or 'Mary went to the office' but not both.
invalid_hypothesis: It is certain that either 'Sandra left the milk' or 'Mary went to the office' 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
    0.95::factA.
    0.1::factB.
    0.1::factC.
    %hop1
    0.9::factX:-or(factC,factB).
    0.5::factY:-and(factC,factA).
    0.95::factZ:-and(factC,factA).
  
    %hop2
    conclusion:-xor(factZ,factX).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Sandra left the milk' or 'Mary went to the office' but not both.