context: It is probably not the case that Lily is white. It is highly likely that Julius is a swan. It is certain that Gertrude is a wolf. We doubt that if 'Gertrude is a wolf' or 'Julius is a swan' or both then Bernhard is gray. Chances are slight that if either 'Gertrude is a wolf' or 'Lily is white' but not both then Sandra left the milk. It is almost certain that if 'Julius is a swan and Gertrude is a wolf' then Mary went to the bedroom.
hypothesis: It is likely that either 'Bernhard is gray' or 'Mary went to the bedroom' but not both.
valid_hypothesis: It is likely that either 'Bernhard is gray' or 'Mary went to the bedroom' but not both.
invalid_hypothesis: It is probably not the case that either 'Bernhard is gray' or 'Mary went to the bedroom' 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.
    0.9::factB.
    1.0::factC.
    %hop1
    0.2::factX:-or(factC,factB).
    0.1::factY:-xor(factC,factA).
    0.95::factZ:-and(factB,factC).
  
    %hop2
    conclusion:-xor(factX,factZ).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Bernhard is gray' or 'Mary went to the bedroom' but not both.