context: We doubt that John went to the garden. It is almost certain that Julius is a frog. There is little chance that Bernhard is a swan. We doubt that if 'Julius is a frog' or 'Bernhard is a swan' or both then Lily is yellow. We believe that if either 'Bernhard is a swan' or 'John went to the garden' but not both then Fred dropped the milk. It is likely that if 'John went to the garden and Bernhard is a swan' then Mary left the football.
hypothesis: There is little chance that either 'Bernhard is a swan' or 'Mary left the football' but not both.
valid_hypothesis: There is little chance that either 'Bernhard is a swan' or 'Mary left the football' but not both.
invalid_hypothesis: It is likely that either 'Bernhard is a swan' or 'Mary left the football' 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
    0.2::factA.
    0.95::factB.
    0.1::factC.
    %hop1
    0.2::factX:-or(factB,factC).
    0.75::factY:-xor(factC,factA).
    0.7::factZ:-and(factA,factC).
  
    %hop2
    conclusion:-xor(factC,factZ).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Bernhard is a swan' or 'Mary left the football' but not both.