MPI-INF/SWS Research Reports 1991-2021

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Quantifier elimination in second-order predicate logic

Gabbay, Dov M. and Ohlbach, Hans Jürgen

July 1992, 18 pages.

Status: available - back from printing

An algorithm is presented which eliminates second-order quantifiers over predicate variables in formulae of type exists P1 ,..., Pn F where F is an arbitrary formula of first--order predicate logic. The resulting formula is equivalent to the original formula - if the algorithm terminates. The algorithm can for example be applied to do interpolation, to eliminate the second--order quantifiers in circumscription, to compute the correlations between structures and power structures, to compute semantic properties corresponding to Hilbert axioms in non classical logics and to compute model theoretic semantics for new logics.

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  AUTHOR = {Gabbay, Dov M. and Ohlbach, Hans J{\"u}rgen},
  TITLE = {Quantifier elimination in second-order predicate logic},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-92-231},
  MONTH = {July},
  YEAR = {1992},
  ISSN = {0946-011X},