  Bernays introduced a method for proving underivability results in
propositional calculi by truth tables. In general, this motivates an
investigations of how to find, given a propositional logic, a finite-valued
logic which has as few tautologies as possible, but which has all the valid
formulas of the given logic as tautologies. It is investigated how far this
method can be carried using (1) one or (2) an infinite sequence of
finite-valued logics. It is shown that the best candidate matrices for (1) can
be computed from a calculus, and how sequences for (2) can be found for certain
classes of logics (including, in particular, logics characterized by Kripke
semantics).
