It is probable that Mary picked up the milk. We doubt that John dropped the apple. It is impossible that Julius is a frog. Chances are slight that if 'Mary picked up the milk' or 'John dropped the apple' or both then Greg is a lion. It is improbable that if 'Mary picked up the milk' or 'John dropped the apple' or both then Daniel took the football. It is impossible that if 'Julius is a frog and Mary picked up the milk' then Lily is yellow.
It is probable that either 'Lily is yellow' or 'Mary picked up the milk' but not both.
It is probable that either 'Lily is yellow' or 'Mary picked up the milk' but not both.
There is almost no chance that either 'Lily is yellow' or 'Mary picked up the milk' but not both.

  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
  0.7::factA.
  0.2::factB.
  0.0::factC.
  %hop1
  0.1::factX:-or(factA,factB).
  0.1::factY:-or(factA,factB).
  0.0::factZ:-and(factC,factA).

  %hop2
  conclusion:-xor(factZ,factA).

  query(conclusion).
  
Either 'Lily is yellow' or 'Mary picked up the milk' but not both.