context: There is almost no chance that Greg is a rhino. It is likely that Gertrude is a sheep. There is a better than even chance that John left the football. There is a very good chance that if 'Gertrude is a sheep and Greg is a rhino' then Sandra got the milk. It is probably the case that if either 'Gertrude is a sheep' or 'Greg is a rhino' but not both then Julius is yellow. There is a better than even chance that if 'John left the football and Greg is a rhino' then Mary went to the kitchen.
hypothesis: It is impossible that either 'Julius is yellow' or 'Greg is a rhino' but not both.
valid_hypothesis: Chances are about even that either 'Julius is yellow' or 'Greg is a rhino' but not both.
invalid_hypothesis: It is impossible that either 'Julius is yellow' or 'Greg is a rhino' 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
    0.02::factA.
    0.7::factB.
    0.6::factC.
    %hop1
    0.8::factX:-and(factB,factA).
    0.7::factY:-xor(factB,factA).
    0.6::factZ:-and(factC,factA).
  
    %hop2
    conclusion:-xor(factY,factA).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Julius is yellow' or 'Greg is a rhino' but not both.