context: It is probably not the case that Daniel left the milk. Chances are slight that Bill moved to the office. Chances are slight that Lily is a swan. It is probable that if 'Bill moved to the office and Lily is a swan' then Julius is white. It is probable that if 'Daniel left the milk' or 'Lily is a swan' or both then Yann is hungry. It is improbable that if either 'Bill moved to the office' or 'Lily is a swan' but not both then Bernhard is a frog.
hypothesis: We believe that either 'Bernhard is a frog' or 'Bill moved to the office' but not both.
valid_hypothesis: It is improbable that either 'Bernhard is a frog' or 'Bill moved to the office' but not both.
invalid_hypothesis: We believe that either 'Bernhard is a frog' or 'Bill moved 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
    0.25::factA.
    0.1::factB.
    0.1::factC.
    %hop1
    0.7::factX:-and(factB,factC).
    0.7::factY:-or(factA,factC).
    0.1::factZ:-xor(factB,factC).
  
    %hop2
    conclusion:-xor(factZ,factB).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Bernhard is a frog' or 'Bill moved to the office' but not both.