There is almost no chance that Brian is gray. It is likely that Mary went to the office. It is probably the case that Winona is a cat. We believe that if 'Winona is a cat' or 'Mary went to the office' or both then John put down the apple. It is impossible that if 'Brian is gray and Mary went to the office' then Lily is a frog. It is probable that if 'Brian is gray' or 'Mary went to the office' or both then Sandra left the milk.
It is likely that either 'Winona is a cat' or 'Lily is a frog' but not both.
It is likely that either 'Winona is a cat' or 'Lily is a frog' but not both.
It is probably not the case that either 'Winona is a cat' or 'Lily is a frog' 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
  0.02::factA.
  0.7::factB.
  0.7::factC.
  %hop1
  0.75::factX:-or(factC,factB).
  0.0::factY:-and(factA,factB).
  0.7::factZ:-or(factA,factB).

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

  query(conclusion).
  
Either 'Winona is a cat' or 'Lily is a frog' but not both.