context: There is little chance that Bernhard is yellow. It is impossible that Julius is a frog. It is probably the case that John left the football. It is improbable that if 'Bernhard is yellow' or 'Julius is a frog' or both then Greg is yellow. It is improbable that if 'Julius is a frog' or 'Bernhard is yellow' or both then Daniel got the milk. We believe that if 'Julius is a frog and Bernhard is yellow' then Mary went to the hallway.
hypothesis: There is almost no chance that either 'Mary went to the hallway' or 'Daniel got the milk' but not both.
valid_hypothesis: There is almost no chance that either 'Mary went to the hallway' or 'Daniel got the milk' but not both.
invalid_hypothesis: It is likely that either 'Mary went to the hallway' or 'Daniel got the milk' 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.
    0.0::factB.
    0.7::factC.
    %hop1
    0.1::factX:-or(factA,factB).
    0.1::factY:-or(factB,factA).
    0.75::factZ:-and(factB,factA).
  
    %hop2
    conclusion:-xor(factZ,factY).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Mary went to the hallway' or 'Daniel got the milk' but not both.