It is impossible that Mary went to the office. We believe that Jeff put down the milk. We doubt that Emily is a mouse. There is a very good chance that if either 'Jeff put down the milk' or 'Emily is a mouse' but not both then Julius is white. It is probably not the case that if either 'Emily is a mouse' or 'Mary went to the office' but not both then Greg is yellow. It is probable that if 'Emily is a mouse' or 'Mary went to the office' or both then Bernhard is gray.
We believe that either 'Emily is a mouse' or 'Mary went to the office' but not both.
We doubt that either 'Emily is a mouse' or 'Mary went to the office' but not both.
We believe that either 'Emily is a mouse' or 'Mary went to the office' 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.
  0.75::factB.
  0.2::factC.
  %hop1
  0.8::factX:-xor(factB,factC).
  0.25::factY:-xor(factC,factA).
  0.7::factZ:-or(factC,factA).

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

  query(conclusion).
  
Either 'Emily is a mouse' or 'Mary went to the office' but not both.