PP-2006-31: Partially ordered connectives and Sigma-1-1 on finite models

PP-2006-31: Sevenster, Merlijn and Tulenheimo, Tero (2006) Partially ordered connectives and Sigma-1-1 on finite models. [Report]

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Abstract

In this paper we take up the study of Henkin quantifiers with boolean variables also known as partially ordered connectives. 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 Sigma-1-1-hearts whose formulae do not allow for existential variables being argument of predicate variables. We show that \Sigma-1-1-hearts 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 Sigma-1-1 , thus we show.

Item Type: Report
Report Nr: PP-2006-31
Series Name: Prepublication (PP) Series
Year: 2006
Uncontrolled Keywords: Henkin quantifiers, finite model theory; NP vs. coNP; partially ordered connectives
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/206

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