Chances are about even that John discarded the apple. Chances are about even that Mary got the football. It is probably the case that Fred went to the garden. It is likely that if either 'John discarded the apple' or 'Mary got the football' but not both then Jason is tired. It is highly unlikely that if either 'Fred went to the garden' or 'Mary got the football' but not both then Bernhard is gray. It is improbable that if either 'Mary got the football' or 'Fred went to the garden' but not both then Brian is white.
It is probably the case that either 'Jason is tired' or 'Brian is white' but not both.
It is probably not the case that either 'Jason is tired' or 'Brian is white' but not both.
It is probably the case that either 'Jason is tired' 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
  0.5::factA.
  0.5::factB.
  0.7::factC.
  %hop1
  0.7::factX:-xor(factA,factB).
  0.05::factY:-xor(factC,factB).
  0.1::factZ:-xor(factB,factC).

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

  query(conclusion).
  
Either 'Jason is tired' or 'Brian is white' but not both.