It is likely that John left the football. It is improbable that Mary went to the hallway. Chances are about even that Gertrude is a sheep. It is likely that if 'Mary went to the hallway and John left the football' then Greg is a rhino. We believe that if 'Mary went to the hallway' or 'Gertrude is a sheep' or both then Bernhard is white. Chances are slight that if 'Mary went to the hallway' or 'Gertrude is a sheep' or both then Bill moved to the office.
It is probably not the case that either 'John left the football' or 'Mary went to the hallway' but not both.
It is probable that either 'John left the football' or 'Mary went to the hallway' but not both.
It is probably not the case that either 'John left the football' 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
  0.7::factA.
  0.1::factB.
  0.5::factC.
  %hop1
  0.7::factX:-and(factB,factA).
  0.75::factY:-or(factB,factC).
  0.1::factZ:-or(factB,factC).

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

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