We believe that Mary went to the hallway. It is probably the case that Brian is white. It is probable that Sandra left the milk. It is probable that if 'Brian is white and Mary went to the hallway' then Emily is a mouse. It is impossible that if 'Brian is white' or 'Mary went to the hallway' or both then Julius is a swan. It is certain that if 'Brian is white and Mary went to the hallway' then John moved to the garden.
Chances are about even that either 'Brian is white' or 'Mary went to the hallway' but not both.
Chances are about even that either 'Brian is white' or 'Mary went to the hallway' but not both.
It is certain that either 'Brian is white' or 'Mary went to the hallway' 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
  0.75::factA.
  0.7::factB.
  0.7::factC.
  %hop1
  0.7::factX:-and(factB,factA).
  0.0::factY:-or(factB,factA).
  1.0::factZ:-and(factB,factA).

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

  query(conclusion).
  
Either 'Brian is white' or 'Mary went to the hallway' but not both.