It is impossible that John discarded the milk. Chances are about even that Julius is a frog. There is a very good chance that Jeff left the apple. There is little chance that if 'Jeff left the apple and Julius is a frog' then Bernhard is a frog. It is certain that if 'Julius is a frog and John discarded the milk' then Greg is white. It is highly unlikely that if 'Julius is a frog' or 'Jeff left the apple' or both then Lily is a swan.
There is little chance that either 'Lily is a swan' or 'Bernhard is a frog' but not both.
There is little chance that either 'Lily is a swan' or 'Bernhard is a frog' but not both.
It is probably the case that either 'Lily is a swan' or 'Bernhard is a frog' 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
  0.0::factA.
  0.5::factB.
  0.8::factC.
  %hop1
  0.1::factX:-and(factC,factB).
  1.0::factY:-and(factB,factA).
  0.05::factZ:-or(factB,factC).

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

  query(conclusion).
  
Either 'Lily is a swan' or 'Bernhard is a frog' but not both.