context: We doubt that Lily is a swan. It is probably not the case that Gertrude is a cat. It is probable that Mary left the milk. It is highly likely that if 'Mary left the milk and Lily is a swan' then John moved to the office. There is little chance that if 'Lily is a swan' or 'Mary left the milk' or both then Daniel dropped the apple. It is impossible that if either 'Lily is a swan' or 'Mary left the milk' but not both then Brian is a frog.
hypothesis: We believe that either 'Gertrude is a cat' or 'Brian is a frog' but not both.
valid_hypothesis: It is probably not the case that either 'Gertrude is a cat' or 'Brian is a frog' but not both.
invalid_hypothesis: We believe that either 'Gertrude is a cat' or 'Brian is a frog' 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
    0.2::factA.
    0.25::factB.
    0.7::factC.
    %hop1
    0.9::factX:-and(factC,factA).
    0.1::factY:-or(factA,factC).
    0.0::factZ:-xor(factA,factC).
  
    %hop2
    conclusion:-xor(factB,factZ).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Gertrude is a cat' or 'Brian is a frog' but not both.