context: It is likely that Sandra dropped the apple. It is certain that Bernhard is gray. It is unlikely that Lily is a swan. It is probable that if 'Lily is a swan and Bernhard is gray' then Jessica is a sheep. It is probably not the case that if 'Lily is a swan and Bernhard is gray' then Julius is a lion. It is certain that if 'Bernhard is gray' or 'Sandra dropped the apple' or both then Mary left the football.
hypothesis: There is little chance that either 'Lily is a swan' or 'Sandra dropped the apple' but not both.
valid_hypothesis: There is a better than even chance that either 'Lily is a swan' or 'Sandra dropped the apple' but not both.
invalid_hypothesis: There is little chance that either 'Lily is a swan' or 'Sandra dropped the apple' 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
    0.7::factA.
    1.0::factB.
    0.2::factC.
    %hop1
    0.7::factX:-and(factC,factB).
    0.25::factY:-and(factC,factB).
    1.0::factZ:-or(factB,factA).
  
    %hop2
    conclusion:-xor(factC,factA).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Lily is a swan' or 'Sandra dropped the apple' but not both.