context: It is certain that Sandra grabbed the milk. It is likely that Lily is yellow. It is improbable that Greg is a swan. It is certain that if 'Sandra grabbed the milk' or 'Lily is yellow' or both then Jessica is a mouse. It is probably the case that if 'Lily is yellow and Sandra grabbed the milk' then Bernhard is gray. There is a better than even chance that if 'Lily is yellow' or 'Greg is a swan' or both then John moved to the office.
hypothesis: It is impossible that either 'Sandra grabbed the milk' or 'Jessica is a mouse' but not both.
valid_hypothesis: It is impossible that either 'Sandra grabbed the milk' or 'Jessica is a mouse' but not both.
invalid_hypothesis: Chances are about even that either 'Sandra grabbed the milk' or 'Jessica is a mouse' but not 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
    1.0::factA.
    0.7::factB.
    0.1::factC.
    %hop1
    1.0::factX:-or(factA,factB).
    0.7::factY:-and(factB,factA).
    0.6::factZ:-or(factB,factC).
  
    %hop2
    conclusion:-xor(factA,factX).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Sandra grabbed the milk' or 'Jessica is a mouse' but not both.