It is certain that Gertrude is a cat. It is probably not the case that Mary left the football. There is a better than even chance that John went to the hallway. There is a very good chance that if 'Mary left the football' or 'John went to the hallway' or both then Lily is a rhino. Chances are about even that if 'Mary left the football and John went to the hallway' then Brian is gray. We doubt that if 'Gertrude is a cat and Mary left the football' then Antoine is hungry.
It is unlikely that either 'John went to the hallway' or 'Lily is a rhino' but not both.
It is unlikely that either 'John went to the hallway' or 'Lily is a rhino' but not both.
There is a very good chance that either 'John went to the hallway' or 'Lily is a rhino' 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
  1.0::factA.
  0.25::factB.
  0.6::factC.
  %hop1
  0.8::factX:-or(factB,factC).
  0.5::factY:-and(factB,factC).
  0.2::factZ:-and(factA,factB).

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

  query(conclusion).
  
Either 'John went to the hallway' or 'Lily is a rhino' but not both.