context: It is almost certain that Julius is a frog. It is certain that Greg is a swan. It is impossible that Brian is green. It is probable that if 'Julius is a frog and Brian is green' then Mary took the milk. We doubt that if 'Greg is a swan' or 'Brian is green' or both then John went to the kitchen. It is likely that if either 'Brian is green' or 'Greg is a swan' but not both then Bernhard is gray.
hypothesis: There is a better than even chance that either 'John went to the kitchen' or 'Bernhard is gray' but not both.
valid_hypothesis: There is a better than even chance that either 'John went to the kitchen' or 'Bernhard is gray' but not both.
invalid_hypothesis: It is impossible that either 'John went to the kitchen' or 'Bernhard is gray' 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.
    1.0::factB.
    0.0::factC.
    %hop1
    0.7::factX:-and(factA,factC).
    0.2::factY:-or(factB,factC).
    0.7::factZ:-xor(factC,factB).
  
    %hop2
    conclusion:-xor(factY,factZ).
  
    query(conclusion).
    
hypothesis_assertion: Either 'John went to the kitchen' or 'Bernhard is gray' but not both.