context: We believe that Greg is a swan. Chances are about even that Bernhard is a frog. Chances are about even that Emily is a mouse. It is probably the case that if 'Greg is a swan' or 'Bernhard is a frog' or both then Mary went to the garden. We believe that if either 'Greg is a swan' or 'Bernhard is a frog' but not both then Sandra dropped the milk. It is probably not the case that if 'Emily is a mouse' or 'Greg is a swan' or both then John got the apple.
hypothesis: It is certain that either 'Bernhard is a frog' or 'Mary went to the garden' but not both.
valid_hypothesis: Chances are about even that either 'Bernhard is a frog' or 'Mary went to the garden' but not both.
invalid_hypothesis: It is certain that either 'Bernhard is a frog' or 'Mary 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
    0.75::factA.
    0.5::factB.
    0.5::factC.
    %hop1
    0.7::factX:-or(factA,factB).
    0.75::factY:-xor(factA,factB).
    0.25::factZ:-or(factC,factA).
  
    %hop2
    conclusion:-xor(factB,factX).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Bernhard is a frog' or 'Mary went to the garden' but not both.