context: It is unlikely that Julius is a swan. It is probably not the case that Brian is green. Chances are about even that Mary picked up the milk. We believe that if 'Julius is a swan and Brian is green' then Daniel left the apple. We believe that if 'Mary picked up the milk' or 'Julius is a swan' or both then John went to the garden. There is little chance that if either 'Brian is green' or 'Julius is a swan' but not both then Bernhard is gray.
hypothesis: It is impossible that 'John went to the garden and Mary picked up the milk'.
valid_hypothesis: Chances are about even that 'John went to the garden and Mary picked up the milk'.
invalid_hypothesis: It is impossible that 'John went to the garden and Mary picked up the milk'.
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.
    0.25::factB.
    0.5::factC.
    %hop1
    0.75::factX:-and(factA,factB).
    0.75::factY:-or(factC,factA).
    0.1::factZ:-xor(factB,factA).
  
    %hop2
    conclusion:-and(factY,factC).
  
    query(conclusion).
    
hypothesis_assertion: 'John went to the garden and Mary picked up the milk'.