context: It is probable that Brian is a rhino. Chances are slight that Mary went to the hallway. There is a very good chance that John dropped the apple. It is almost certain that if 'John dropped the apple' or 'Mary went to the hallway' or both then Julius is a frog. It is highly unlikely that if either 'Brian is a rhino' or 'Mary went to the hallway' but not both then Bernhard is yellow. It is impossible that if 'John dropped the apple' or 'Brian is a rhino' or both then Greg is a lion.
hypothesis: We believe that either 'Julius is a frog' or 'Bernhard is yellow' but not both.
valid_hypothesis: We believe that either 'Julius is a frog' or 'Bernhard is yellow' but not both.
invalid_hypothesis: It is improbable that either 'Julius is a frog' or 'Bernhard is yellow' 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.
    0.1::factB.
    0.8::factC.
    %hop1
    0.95::factX:-or(factC,factB).
    0.05::factY:-xor(factA,factB).
    0.0::factZ:-or(factC,factA).
  
    %hop2
    conclusion:-xor(factX,factY).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Julius is a frog' or 'Bernhard is yellow' but not both.