context: There is almost no chance that Mary grabbed the milk. We believe that Lily is white. It is probably not the case that Gertrude is a wolf. Chances are slight that if either 'Mary grabbed the milk' or 'Lily is white' but not both then Brian is a rhino. It is probable that if 'Lily is white and Gertrude is a wolf' then Bernhard is gray. It is highly unlikely that if 'Mary grabbed the milk and Lily is white' then John took the apple.
hypothesis: We believe that either 'John took the apple' or 'Mary grabbed the milk' but not both.
valid_hypothesis: There is almost no chance that either 'John took the apple' or 'Mary grabbed the milk' but not both.
invalid_hypothesis: We believe that either 'John took the apple' or 'Mary grabbed the milk' 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
    0.02::factA.
    0.75::factB.
    0.25::factC.
    %hop1
    0.1::factX:-xor(factA,factB).
    0.7::factY:-and(factB,factC).
    0.05::factZ:-and(factA,factB).
  
    %hop2
    conclusion:-xor(factZ,factA).
  
    query(conclusion).
    
hypothesis_assertion: Either 'John took the apple' or 'Mary grabbed the milk' but not both.