context: It is unlikely that John picked up the milk. There is almost no chance that Julius is yellow. It is likely that Lily is a rhino. Chances are about even that if 'John picked up the milk and Julius is yellow' then Bernhard is a frog. It is probable that if 'John picked up the milk' or 'Lily is a rhino' or both then Brian is green. Chances are slight that if either 'Julius is yellow' or 'John picked up the milk' but not both then Jason is thirsty.
hypothesis: It is impossible that 'Julius is yellow and Bernhard is a frog'.
valid_hypothesis: It is impossible that 'Julius is yellow and Bernhard is a frog'.
invalid_hypothesis: There is a very good chance that 'Julius is yellow and Bernhard is a frog'.
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.
    0.02::factB.
    0.7::factC.
    %hop1
    0.5::factX:-and(factA,factB).
    0.7::factY:-or(factA,factC).
    0.1::factZ:-xor(factB,factA).
  
    %hop2
    conclusion:-and(factB,factX).
  
    query(conclusion).
    
hypothesis_assertion: 'Julius is yellow and Bernhard is a frog'.