PP-2006-53: Finite model theory for partially ordered connectives

PP-2006-53: Sevenster, Merlijn and Tulenheimo, Tero (2006) Finite model theory for partially ordered connectives. [Report]

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Abstract

In the present article a study of the finite model theory of Henkin quantifiers with boolean variables, a.k.a. partially ordered connectives, is undertaken. The logic of first-order formulae prefixed by partially ordered connectives, denoted D, is considered on finite structures. D is characterized as a fragment of second-order existential logic \Sigma^1_1; the formulae of the relevant fragment do not allow existentially quantified variables as arguments of predicate variables. Using this characterization result, D is shown to harbor a strict hierarchy induced by the arity of predicate variables. Further, D is shown to capture NP over linearly ordered structures, and not to be closed under complementation. We conclude with a comparison between the logics D and \Sigma^1_1 on several metatheoretical properties.

Item Type: Report
Report Nr: PP-2006-53
Series Name: Prepublication (PP) Series
Year: 2006
Uncontrolled Keywords: descriptive complexity, computational complexity, partially ordered quantification
Subjects: Computation
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/228

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