context: We doubt that John went to the office. We doubt that Mary got the football. We doubt that Sandra left the milk. Chances are about even that if 'Sandra left the milk and John went to the office' then Lily is green. It is almost certain that if either 'John went to the office' or 'Mary got the football' but not both then Julius is a frog. It is improbable that if 'John went to the office and Sandra left the milk' then Bernhard is a swan.
hypothesis: It is impossible that 'Julius is a frog and Bernhard is a swan'.
valid_hypothesis: It is impossible that 'Julius is a frog and Bernhard is a swan'.
invalid_hypothesis: We believe that 'Julius is a frog and Bernhard is a swan'.
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
    0.2::factA.
    0.2::factB.
    0.2::factC.
    %hop1
    0.5::factX:-and(factC,factA).
    0.95::factY:-xor(factA,factB).
    0.1::factZ:-and(factA,factC).
  
    %hop2
    conclusion:-and(factY,factZ).
  
    query(conclusion).
    
hypothesis_assertion: 'Julius is a frog and Bernhard is a swan'.