context: Chances are about even that Greg is a swan. There is little chance that Julius is a frog. It is highly unlikely that Bernhard is gray. There is little chance that if either 'Bernhard is gray' or 'Julius is a frog' but not both then Brian is white. It is improbable that if either 'Bernhard is gray' or 'Julius is a frog' but not both then Mary dropped the apple. It is certain that if 'Bernhard is gray' or 'Julius is a frog' or both then Bill went to the bedroom.
hypothesis: It is impossible that 'Mary dropped the apple and Julius is a frog'.
valid_hypothesis: It is impossible that 'Mary dropped the apple and Julius is a frog'.
invalid_hypothesis: Chances are about even that 'Mary dropped the apple and Julius 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
    0.5::factA.
    0.1::factB.
    0.05::factC.
    %hop1
    0.1::factX:-xor(factC,factB).
    0.1::factY:-xor(factC,factB).
    1.0::factZ:-or(factC,factB).
  
    %hop2
    conclusion:-and(factY,factB).
  
    query(conclusion).
    
hypothesis_assertion: 'Mary dropped the apple and Julius is a frog'.