context: It is improbable that Julius is white. We doubt that Bernhard is green. We doubt that Brian is a lion. There is little chance that if either 'Julius is white' or 'Brian is a lion' but not both then Lily is a rhino. It is probably not the case that if 'Julius is white and Brian is a lion' then Sandra got the milk. It is highly unlikely that if 'Bernhard is green and Julius is white' then Bill went to the garden.
hypothesis: It is improbable that either 'Julius is white' or 'Bill went to the garden' but not both.
valid_hypothesis: It is improbable that either 'Julius is white' or 'Bill went to the garden' but not both.
invalid_hypothesis: It is likely that either 'Julius is white' or 'Bill went to the garden' 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.
    0.2::factB.
    0.2::factC.
    %hop1
    0.1::factX:-xor(factA,factC).
    0.25::factY:-and(factA,factC).
    0.05::factZ:-and(factB,factA).
  
    %hop2
    conclusion:-xor(factA,factZ).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Julius is white' or 'Bill went to the garden' but not both.