context: There is a very good chance that Emily is a wolf. It is probably the case that Mary picked up the milk. It is probable that John moved to the office. Chances are slight that if 'Emily is a wolf and John moved to the office' then Gertrude is a mouse. It is improbable that if either 'Emily is a wolf' or 'Mary picked up the milk' but not both then Bernhard is a frog. It is probable that if 'Mary picked up the milk' or 'John moved to the office' or both then Fred left the apple.
hypothesis: It is probable that either 'Bernhard is a frog' or 'Mary picked up the milk' but not both.
valid_hypothesis: It is probable that either 'Bernhard is a frog' or 'Mary picked up the milk' but not both.
invalid_hypothesis: We doubt that either 'Bernhard is a frog' or 'Mary picked up the milk' 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
    0.8::factA.
    0.7::factB.
    0.7::factC.
    %hop1
    0.1::factX:-and(factA,factC).
    0.1::factY:-xor(factA,factB).
    0.7::factZ:-or(factB,factC).
  
    %hop2
    conclusion:-xor(factY,factB).
  
    query(conclusion).
    
hypothesis_assertion: Either 'Bernhard is a frog' or 'Mary picked up the milk' but not both.