Quantifier Elimination in Second-Order Predicate Logic.
Dov M. Gabbay, Hans Jürgen Ohlbach · 1992
An algorithm is presented which eliminates second-order quantiers over predicate variables in formulae of type 9P 1 ; . . . ; Pn where 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 quantiers 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. An earlier version of the paper has been published in [GO92b].