context: There is little chance that John went to the hallway. It is improbable that Mary moved to the office. We believe that Lily is a swan. There is a very good chance that if either 'Lily is a swan' or 'Mary moved to the office' but not both then Daniel got the milk. It is impossible that if 'Lily is a swan and Mary moved to the office' then Julius is a lion. There is a very good chance that if either 'Mary moved to the office' or 'John went to the hallway' but not both then Bernhard is gray.
hypothesis: There is little chance that either 'Bernhard is gray' or 'John went to the hallway' but not both.
valid_hypothesis: There is little chance that either 'Bernhard is gray' or 'John went to the hallway' but not both.
invalid_hypothesis: It is probable that either 'Bernhard is gray' or 'John went to the hallway' 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
    0.1::factA.
    0.1::factB.
    0.75::factC.
    %hop1
    0.8::factX:-xor(factC,factB).
    0.0::factY:-and(factC,factB).
    0.8::factZ:-xor(factB,factA).
  
    %hop2
    conclusion:-xor(factZ,factA).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Bernhard is gray' or 'John went to the hallway' but not both.