Chances are about even that Brian is yellow. There is a very good chance that Sandra put down the milk. Chances are about even that Antoine is hungry. We believe that if 'Antoine is hungry' or 'Sandra put down the milk' or both then Bernhard is a frog. It is probably not the case that if either 'Sandra put down the milk' or 'Antoine is hungry' but not both then Greg is white. It is probably the case that if either 'Antoine is hungry' or 'Sandra put down the milk' but not both then John picked up the apple.
We doubt that 'Brian is yellow and John picked up the apple'.
We doubt that 'Brian is yellow and John picked up the apple'.
It is probable that 'Brian is yellow and John picked up the apple'.

  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.
  0.8::factB.
  0.5::factC.
  %hop1
  0.75::factX:-or(factC,factB).
  0.25::factY:-xor(factB,factC).
  0.7::factZ:-xor(factC,factB).

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

  query(conclusion).
  
'Brian is yellow and John picked up the apple'.