It is highly likely that Julius is a frog. There is little chance that Mary went to the kitchen. We believe that Winona is a sheep. It is probably the case that if 'Julius is a frog and Winona is a sheep' then Jessica is a cat. It is highly unlikely that if 'Mary went to the kitchen' or 'Winona is a sheep' or both then Brian is white. It is highly unlikely that if 'Mary went to the kitchen and Julius is a frog' then John left the football.
Chances are about even that either 'Jessica is a cat' or 'Brian is white' but not both.
Chances are about even that either 'Jessica is a cat' or 'Brian is white' but not both.
There is almost no chance that either 'Jessica is a cat' or 'Brian is white' 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
  0.9::factA.
  0.1::factB.
  0.75::factC.
  %hop1
  0.7::factX:-and(factA,factC).
  0.05::factY:-or(factB,factC).
  0.05::factZ:-and(factB,factA).

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

  query(conclusion).
  
Either 'Jessica is a cat' or 'Brian is white' but not both.