Chances are slight that Brian is a frog. Chances are slight that Jessica is a sheep. We doubt that Mary picked up the apple. Chances are about even that if 'Brian is a frog and Mary picked up the apple' then John took the football. Chances are slight that if either 'Jessica is a sheep' or 'Mary picked up the apple' but not both then Greg is yellow. It is almost certain that if 'Brian is a frog and Mary picked up the apple' then Julius is gray.
It is probable that either 'Brian is a frog' or 'Julius is gray' but not both.
There is little chance that either 'Brian is a frog' or 'Julius is gray' but not both.
It is probable that either 'Brian is a frog' or 'Julius is gray' 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
  0.1::factA.
  0.1::factB.
  0.2::factC.
  %hop1
  0.5::factX:-and(factA,factC).
  0.1::factY:-xor(factB,factC).
  0.95::factZ:-and(factA,factC).

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

  query(conclusion).
  
Either 'Brian is a frog' or 'Julius is gray' but not both.