context: It is probably not the case that Brian is a rhino. There is almost no chance that John went to the hallway. There is almost no chance that Jeff moved to the garden. We believe that if 'Brian is a rhino' or 'John went to the hallway' or both then Mary put down the apple. Chances are about even that if 'John went to the hallway and Brian is a rhino' then Jessica is a cat. We believe that if 'Jeff moved to the garden' or 'Brian is a rhino' or both then Lily is a frog.
hypothesis: It is probable that either 'John went to the hallway' or 'Mary put down the apple' but not both.
valid_hypothesis: It is unlikely that either 'John went to the hallway' or 'Mary put down the apple' but not both.
invalid_hypothesis: It is probable that either 'John went to the hallway' or 'Mary put down 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
    0.25::factA.
    0.02::factB.
    0.02::factC.
    %hop1
    0.75::factX:-or(factA,factB).
    0.5::factY:-and(factB,factA).
    0.75::factZ:-or(factC,factA).
  
    %hop2
    conclusion:-xor(factB,factX).
  
    query(conclusion).
    
hypothesis_assertion: Either 'John went to the hallway' or 'Mary put down the apple' but not both.