Quantifier elimination in elementary set theory

Authors:
Ewa Orłowska;Andrzej Szałas
Affiliations:
National Institute of Telecommunications, Warsaw, Poland;The University of Economics and Computer Science, Olsztyn, Poland
Venue:
RelMiCS'05 Proceedings of the 8th international conference on Relational Methods in Computer Science, Proceedings of the 3rd international conference on Applications of Kleene Algebra
Year:
2005

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Abstract

In the current paper we provide two methods for quantifier elimination applicable to a large class of formulas of the elementary set theory. The first one adapts the Ackermann method [1] and the second one adapts the fixpoint method of [20]. We show applications of the proposed techniques in the theory of correspondence between modal logics and elementary set theory. The proposed techniques can also be applied in an automated generation of proof rules based on the semantic-based translation of axioms of a given logic into the elementary set theory.