context: There is little chance that Daniel took the football. It is improbable that Gertrude is a mouse. It is probably not the case that Brian is yellow. It is highly unlikely that if either 'Brian is yellow' or 'Gertrude is a mouse' but not both then John got the milk. We believe that if either 'Gertrude is a mouse' or 'Daniel took the football' but not both then Greg is green. It is probable that if 'Daniel took the football and Brian is yellow' then Bernhard is a frog.
hypothesis: It is probable that 'Brian is yellow' or 'Greg is green' or both.
valid_hypothesis: It is probably not the case that 'Brian is yellow' or 'Greg is green' or both.
invalid_hypothesis: It is probable that 'Brian is yellow' or 'Greg is green' or 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
    0.1::factA.
    0.1::factB.
    0.25::factC.
    %hop1
    0.05::factX:-xor(factC,factB).
    0.75::factY:-xor(factB,factA).
    0.7::factZ:-and(factA,factC).
  
    %hop2
    conclusion:-or(factC,factY).
  
    query(conclusion).
    
hypothesis_assertion: 'Brian is yellow' or 'Greg is green' or both.