@TECHREPORT{Ohlbach+Schmidt+Hustadt@MPII-TR1995.pdf,
 AUTHOR      = {Ohlbach, Hans J{\"u}rgen and Schmidt, Renate A. and 
                Hustadt, Ullrich},
 YEAR        = {1995},
 TITLE       = {Translating Graded Modalities into Predicate Logic},
 TYPE        = {Technical Report},
 NUMBER      = {MPI-I-95-2-008},
 INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
 ADDRESS     = {Saarbr{\"u}cken},
 NOTE        = {Also appeared in H. Wansing, editor, Proof Theory of Modal Logic, 
                Kluwer, 1996.},
 URL         = {Ohlbach+Schmidt+Hustadt@MPII-TR1995.pdf},
 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.},
}

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