context: It is almost certain that Mary went to the hallway. Chances are slight that Fred is in the school. We doubt that Brian is white. Chances are slight that if either 'Fred is in the school' or 'Brian is white' but not both then Bernhard is gray. It is impossible that if 'Mary went to the hallway' or 'Fred is in the school' or both then Daniel got the football. There is little chance that if either 'Fred is in the school' or 'Mary went to the hallway' but not both then John left the milk.
hypothesis: We doubt that either 'Bernhard is gray' or 'Brian is white' but not both.
valid_hypothesis: We doubt that either 'Bernhard is gray' or 'Brian is white' but not both.
invalid_hypothesis: It is probably the case that either 'Bernhard is gray' or 'Brian is white' 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.
    0.2::factC.
    %hop1
    0.1::factX:-xor(factB,factC).
    0.0::factY:-or(factA,factB).
    0.1::factZ:-xor(factB,factA).
  
    %hop2
    conclusion:-xor(factX,factC).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Bernhard is gray' or 'Brian is white' but not both.