There is a very good chance that Lily is a rhino. We believe that John left the football. It is certain that Jessica is a cat. It is improbable that if 'John left the football' or 'Lily is a rhino' or both then Bernhard is gray. It is highly likely that if 'Lily is a rhino' or 'John left the football' or both then Julius is a frog. It is unlikely that if 'Jessica is a cat and John left the football' then Mary went to the hallway.
It is probable that either 'Jessica is a cat' or 'John left the football' but not both.
It is probably not the case that either 'Jessica is a cat' or 'John left the football' but not both.
It is probable that either 'Jessica is a cat' 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
  0.8::factA.
  0.75::factB.
  1.0::factC.
  %hop1
  0.1::factX:-or(factB,factA).
  0.9::factY:-or(factA,factB).
  0.2::factZ:-and(factC,factB).

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

  query(conclusion).
  
Either 'Jessica is a cat' or 'John left the football' but not both.