context: There is a better than even chance that John went to the office. It is improbable that Bernhard is a frog. It is highly unlikely that Brian is yellow. It is probable that if either 'John went to the office' or 'Brian is yellow' but not both then Julius is a lion. It is improbable that if either 'Brian is yellow' or 'Bernhard is a frog' but not both then Mary discarded the milk. It is almost certain that if 'Brian is yellow and Bernhard is a frog' then Winona is a sheep.
hypothesis: It is highly unlikely that either 'Julius is a lion' or 'Mary discarded the milk' but not both.
valid_hypothesis: Chances are about even that either 'Julius is a lion' or 'Mary discarded the milk' but not both.
invalid_hypothesis: It is highly unlikely that either 'Julius is a lion' 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
    0.6::factA.
    0.1::factB.
    0.05::factC.
    %hop1
    0.7::factX:-xor(factA,factC).
    0.1::factY:-xor(factC,factB).
    0.95::factZ:-and(factC,factB).
  
    %hop2
    conclusion:-xor(factX,factY).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Julius is a lion' or 'Mary discarded the milk' but not both.