context: It is improbable that Julius is a frog. There is almost no chance that Mary picked up the milk. We believe that John went to the kitchen. There is a better than even chance that if 'John went to the kitchen' or 'Mary picked up the milk' or both then Jeff moved to the garden. There is little chance that if either 'Mary picked up the milk' or 'John went to the kitchen' but not both then Brian is yellow. It is impossible that if 'Julius is a frog' or 'Mary picked up the milk' or both then Daniel grabbed the apple.
hypothesis: It is almost certain that either 'Julius is a frog' or 'Daniel grabbed the apple' but not both.
valid_hypothesis: There is little chance that either 'Julius is a frog' or 'Daniel grabbed the apple' but not both.
invalid_hypothesis: It is almost certain that either 'Julius is a frog' or 'Daniel grabbed the apple' 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
    0.1::factA.
    0.02::factB.
    0.75::factC.
    %hop1
    0.6::factX:-or(factC,factB).
    0.1::factY:-xor(factB,factC).
    0.0::factZ:-or(factA,factB).
  
    %hop2
    conclusion:-xor(factA,factZ).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Julius is a frog' or 'Daniel grabbed the apple' but not both.