context: It is highly unlikely that Sandra left the apple. There is a very good chance that Lily is white. It is almost certain that Brian is gray. It is almost certain that if 'Sandra left the apple' or 'Lily is white' or both then Bernhard is gray. It is highly unlikely that if 'Sandra left the apple' or 'Lily is white' or both then Julius is yellow. It is improbable that if 'Brian is gray and Lily is white' then Mary went to the office.
hypothesis: It is improbable that either 'Sandra left the apple' or 'Mary went to the office' but not both.
valid_hypothesis: It is improbable that either 'Sandra left the apple' or 'Mary went to the office' but not both.
invalid_hypothesis: There is a better than even chance that either 'Sandra left the apple' 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
    0.05::factA.
    0.8::factB.
    0.95::factC.
    %hop1
    0.95::factX:-or(factA,factB).
    0.05::factY:-or(factA,factB).
    0.1::factZ:-and(factC,factB).
  
    %hop2
    conclusion:-xor(factA,factZ).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Sandra left the apple' or 'Mary went to the office' but not both.