context: It is probably not the case that John took the apple. It is certain that Julius is white. It is highly unlikely that Emily is a sheep. It is certain that if 'Emily is a sheep and Julius is white' then Lily is a rhino. We doubt that if 'John took the apple' or 'Emily is a sheep' or both then Mary went to the bedroom. It is highly unlikely that if either 'John took the apple' or 'Emily is a sheep' but not both then Brian is gray.
hypothesis: It is improbable that either 'Julius is white' or 'Emily is a sheep' but not both.
valid_hypothesis: It is almost certain that either 'Julius is white' or 'Emily is a sheep' but not both.
invalid_hypothesis: It is improbable that either 'Julius is white' or 'Emily is a sheep' 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.
    1.0::factB.
    0.05::factC.
    %hop1
    1.0::factX:-and(factC,factB).
    0.2::factY:-or(factA,factC).
    0.05::factZ:-xor(factA,factC).
  
    %hop2
    conclusion:-xor(factB,factC).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Julius is white' or 'Emily is a sheep' but not both.