context: It is probably not the case that Mary got the apple. We doubt that Bernhard is a swan. It is improbable that Julius is yellow. Chances are about even that if either 'Julius is yellow' or 'Bernhard is a swan' but not both then Brian is a frog. There is little chance that if 'Mary got the apple and Julius is yellow' then Jessica is a sheep. There is almost no chance that if 'Julius is yellow' or 'Mary got the apple' or both then Lily is green.
hypothesis: There is a very good chance that either 'Brian is a frog' or 'Mary got the apple' but not both.
valid_hypothesis: It is probably not the case that either 'Brian is a frog' or 'Mary got the apple' but not both.
invalid_hypothesis: There is a very good chance that either 'Brian is a frog' or 'Mary got 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
    0.25::factA.
    0.2::factB.
    0.1::factC.
    %hop1
    0.5::factX:-xor(factC,factB).
    0.1::factY:-and(factA,factC).
    0.02::factZ:-or(factC,factA).
  
    %hop2
    conclusion:-xor(factX,factA).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Brian is a frog' or 'Mary got the apple' but not both.