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Boolean Dependence Logic and Partially-Ordered Connectives

  • Johannes Ebbing
  • Lauri Hella
  • Peter Lohmann
  • Jonni Virtema
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8071)

Abstract

We introduce a new variant of dependence logic (\(\mathcal{D}\)) called Boolean dependence logic (\(\mathcal{BD}\)). In \(\mathcal{BD}\) dependence atoms are of the type =(x 1,...,x n ,α), where α is a Boolean variable. Intuitively, with Boolean dependence atoms one can express quantification of relations, while standard dependence atoms express quantification over functions.

We compare the expressive power of \(\mathcal{BD}\) to \(\mathcal{D}\) and first-order logic enriched by partially-ordered connectives, \(\mathcal{FO(POC)}\). We show that the expressive power of \(\mathcal{BD}\) and \(\mathcal{D}\) coincide. We define natural syntactic fragments of \(\mathcal{BD}\) and show that they coincide with the corresponding fragments of \(\mathcal{FO(POC)}\) with respect to expressive power. We then show that the fragments form a strict hierarchy.

Keywords

Dependence Logic Partially-Ordered Connectives Expressivity Existential Second-Order Logic 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Johannes Ebbing
    • 1
  • Lauri Hella
    • 2
  • Peter Lohmann
    • 1
  • Jonni Virtema
    • 2
  1. 1.Theoretical Computer ScienceLeibniz University HannoverGermany
  2. 2.Mathematics, School of Information SciencesUniversity of TampereFinland

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