There is little chance that Bill went to the garden. It is impossible that John discarded the apple. It is probably the case that Bernhard is a frog. It is highly likely that if 'Bernhard is a frog and John discarded the apple' then Mary left the football. It is probable that if 'Bernhard is a frog' or 'John discarded the apple' or both then Greg is a frog. Chances are about even that if 'Bill went to the garden' or 'John discarded the apple' or both then Sandra got the football.
It is certain that either 'Greg is a frog' or 'Bill went to the garden' but not both.
Chances are about even that either 'Greg is a frog' or 'Bill went to the garden' but not both.
It is certain that either 'Greg is a frog' or 'Bill went to the garden' 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.
  0.0::factB.
  0.7::factC.
  %hop1
  0.9::factX:-and(factC,factB).
  0.7::factY:-or(factC,factB).
  0.5::factZ:-or(factA,factB).

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

  query(conclusion).
  
Either 'Greg is a frog' or 'Bill went to the garden' but not both.