@INCOLLECTION{OhlbachSchmidtHustadt96,
AUTHOR = {Ohlbach, H. J. and Schmidt, R. A. and Hustadt, U.},
YEAR = {1996},
TITLE = {Translating Graded Modalities into Predicate Logic},
EDITOR = {Wansing, H.},
BOOKTITLE = {Proof Theory of Modal Logic},
SERIES = {Applied Logic Series},
VOLUME = {2},
PUBLISHER = {Kluwer},
PAGES = {253--291},
NOTE = {Also available as Technical Report MPI-I-95-2-008,
Max-Planck-Institut f{\"u}r Informatik, Saarbr{\"u}cken, Germany 
(May 1995)},
ABSTRACT = {In the logic of graded modalities it is possible to talk
about sets of finite cardinality.  Various calculi exist for graded
modal logics and all generate vast amounts of case distinctions.  In
this paper we present an optimized translation from graded modal logic
into many-sorted predicate logic.  This translation has the advantage
that in contrast to known approaches our calculus enables us to reason
with cardinalities of sets symbolically.  In many cases the length of
proofs for theorems of this calculus is independent of the
cardinalities. The translation is sound and complete.},
URL = {http://www.cs.man.ac.uk/~schmidt/publications/MPI-I-95-2-008.ps.gz},
}