Quantifier Elimination in Second-Order Predicate Logic

Gabbay, Dov M.; Ohlbach, Hans Jürgen

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Quantifier Elimination in Second-Order Predicate Logic

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Gabbay, Dov M.
Max Planck Society;

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Ohlbach, Hans Jürgen
Programming Logics, MPI for Informatics, Max Planck Society;

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Gabbay, D. M., & Ohlbach, H. J. (1992). Quantifier Elimination in Second-Order Predicate Logic. South African Computer Journal, 7, 35-43.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-AE1B-8

Abstract

An algorithm is presented which eliminates second-order quantifiers over predicate variables in formulae of type $\exists P_1, \ldots, P_n \psi$ where $\psi$ 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.