@TECHREPORT{OlbachSchmidt-95-mpii2-002,
AUTHOR = {Ohlbach, Hans J{\"u}rgen and Schmidt, Renate A.}, 
YEAR = {January 1995},
TITLE = {Functional Translation and Second-Order Frame Properties of
Modal Logics},
TYPE = {Technical Report},
NUMBER = {MPI-I-95-2-002},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Saarbr{\"u}cken},
NOTE = {Submitted for publication to the {\em Journal of Logic and
Computation}.},
ABSTRACT = {Normal modal logics can be defined axiomatically as Hilbert
systems, or semantically in terms of Kripke's possible worlds and
accessibility relations. Unfortunately there are Hilbert axioms which do
not have corresponding first-order properties for the accessibility
relation. For these logics the standard semantics-based theorem proving
techniques, in particular, the relational translation into first-order
predicate logic, do not work. 

There is an alternative translation, the so-called functional
translation, in which the accessibility relations are replaced by
certain terms which intuitively can be seen as functions mapping worlds
to accessible worlds. In this paper we show that from a certain point of
view this functional language is more expressive than the relational
language, and that certain second-order frame properties can be mapped
to first-order formulae expressed in the functional language.
Moreover, we show how these formulae can be computed automatically from
the Hilbert axioms.   This extends the applicability of the functional
translation method.},
}