context: It is probable that Winona is a sheep. Chances are about even that Lily is a swan. It is highly unlikely that Brian is a frog. It is highly unlikely that if either 'Brian is a frog' or 'Winona is a sheep' but not both then Bernhard is green. We doubt that if either 'Brian is a frog' or 'Lily is a swan' but not both then John went to the kitchen. We doubt that if 'Lily is a swan' or 'Brian is a frog' or both then Mary discarded the milk.
hypothesis: It is improbable that either 'Brian is a frog' or 'Mary discarded the milk' but not both.
valid_hypothesis: It is improbable that either 'Brian is a frog' or 'Mary discarded the milk' but not both.
invalid_hypothesis: It is highly likely that either 'Brian is a frog' or 'Mary discarded 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
    0.7::factA.
    0.5::factB.
    0.05::factC.
    %hop1
    0.05::factX:-xor(factC,factA).
    0.2::factY:-xor(factC,factB).
    0.2::factZ:-or(factB,factC).
  
    %hop2
    conclusion:-xor(factC,factZ).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Brian is a frog' or 'Mary discarded the milk' but not both.