Partially Ordered Connectives and Sum11 on Finite Models

Abstract

In this paper we take up the study of Henkin quantifiers with boolean variables [4] also known as partially ordered connectives [19]. We consider first-order formulae prefixed by partially ordered connectives, denoted D, on finite structures. We characterize D as a fragment of second-order existential logic Σ 1♥ whose formulae do not allow for existential variables being argument of predicate variables. We show that Σ 1♥ harbors a strict hierarchy induced by the arity of predicate variables and that it is not closed under complementation, by means of a game-theoretical argument. Admitting for at most one existential variable to appear as the argument of a predicate variable already yields a logic coinciding with full Σ 1 , thus we show.

DOI: 10.1007/11780342_52

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Cite this paper

@inproceedings{Sevenster2006PartiallyOC, title={Partially Ordered Connectives and Sum11 on Finite Models}, author={Merlijn Sevenster and Tero Tulenheimo}, booktitle={CiE}, year={2006} }