An algorithm is presented which eliminates second-order quantifiers over predicate variables in formulae of type $\exists P_1 ,..., P_n\ F$ 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.
Dualities between different theories occur frequently inmathematics and logic --- between syntax and semantics of a logic, between structures and power structures, between relations and relational algebras, to name just a few. In this paper we show for the case of structures and power structures how corresponding properties of the two related structures can be computed fully automatically by means of quantifier elimination algorithms and predicate logic theorem provers. We illustrate the method with a large number of examples and we give enough technical hints to enable the reader who has access to the {\sc Otter} theorem prover to experiment herself.
The SCAN algorithm has been proposed for second order quantifier elimination. In particular it can be applied to find correspondence axioms for systems of modal logic. Up to now, what has been studied are systems with unary modal operators. 17 In this paper we study how SCAN can be applied to various systems of conditional logic, which are logical systems with binary modal operators.