Chances are about even that Brian is a frog. Chances are about even that John picked up the milk. We doubt that Julius is white. It is likely that if 'Brian is a frog' or 'John picked up the milk' or both then Lily is a lion. There is little chance that if 'Brian is a frog and Julius is white' then Jeff went to the garden. Chances are slight that if 'John picked up the milk' or 'Julius is white' or both then Sandra dropped the apple.
It is probable that either 'Jeff went to the garden' or 'Julius is white' but not both.
It is unlikely that either 'Jeff went to the garden' or 'Julius is white' but not both.
It is probable that either 'Jeff went to the garden' or 'Julius is white' 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
  0.5::factA.
  0.5::factB.
  0.2::factC.
  %hop1
  0.7::factX:-or(factA,factB).
  0.1::factY:-and(factA,factC).
  0.1::factZ:-or(factB,factC).

  %hop2
  conclusion:-xor(factY,factC).

  query(conclusion).
  
Either 'Jeff went to the garden' or 'Julius is white' but not both.