Chances are slight that John left the football. It is almost certain that Emily is a mouse. It is improbable that Greg is green. It is impossible that if 'Emily is a mouse and Greg is green' then Sandra got the milk. Chances are about even that if 'John left the football' or 'Greg is green' or both then Jeff went to the garden. Chances are about even that if 'John left the football and Emily is a mouse' then Brian is yellow.
We believe that either 'Jeff went to the garden' or 'John left the football' but not both.
It is improbable that either 'Jeff went to the garden' or 'John left the football' but not both.
We believe that either 'Jeff went to the garden' or 'John left the football' 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
  0.1::factA.
  0.95::factB.
  0.1::factC.
  %hop1
  0.0::factX:-and(factB,factC).
  0.5::factY:-or(factA,factC).
  0.5::factZ:-and(factA,factB).

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

  query(conclusion).
  
Either 'Jeff went to the garden' or 'John left the football' but not both.