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Modal Logics and Local Quantifiers: A Zoo in the Elementary Hierarchy

Modal Logics and Local Quantifiers: A Zoo in the Elementary Hierarchy

  • Raul Fervari  ORCID: orcid.org/0000-0003-0360-072510 &
  • Alessio Mansutti  ORCID: orcid.org/0000-0002-1104-729911 
  • Conference paper
  • Open Access
  • First Online: 29 March 2022

  • 1369 Accesses

Part of the Lecture Notes in Computer Science book series (LNCS,volume 13242)

Abstract

We study a family of modal logics interpreted on tree-like structures, and featuring local quantifiers \(\exists ^{k}p\) that bind the proposition p to worlds that are accessible from the current one in at most k steps. We consider a first-order and a second-order semantics for the quantifiers, which enables us to relate several well-known formalisms, such as hybrid logics, \(\textsf {S5Q}\) and graded modal logic. To better stress these connections, we explore fragments of our logics, called herein round-bounded fragments. Depending on whether first or second-order semantics is considered, these fragments populate the hierarchy \({2\textsc {NExp} \subset 3\textsc {NExp} \subset \cdots }\) or the hierarchy \({2\textsc {AExp}_{pol} \subset 3\textsc {AExp}_{pol} \subset \cdots }\), respectively. For formulae up-to modal depth k, the complexity improves by one exponential.

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Authors and Affiliations

  1. CONICET and Universidad Nacional de Córdoba, Córdoba, Argentina

    Raul Fervari

  2. Department of Computer Science, University of Oxford, Parks Rd, Oxford, OX1 3QD, UK

    Alessio Mansutti

Authors
  1. Raul Fervari
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  2. Alessio Mansutti
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Corresponding author

Correspondence to Alessio Mansutti .

Editor information

Editors and Affiliations

  1. Université Paris-Saclay, CNRS, ENS Paris-Saclay, Gif-sur-Yvette, France

    Prof. Patricia Bouyer

  2. Friedrich-Alexander-Universität Erlangen, Erlangen, Germany

    Lutz Schröder

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Fervari, R., Mansutti, A. (2022). Modal Logics and Local Quantifiers: A Zoo in the Elementary Hierarchy. In: Bouyer, P., Schröder, L. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2022. Lecture Notes in Computer Science, vol 13242. Springer, Cham. https://doi.org/10.1007/978-3-030-99253-8_16

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  • DOI: https://doi.org/10.1007/978-3-030-99253-8_16

  • Published: 29 March 2022

  • Publisher Name: Springer, Cham

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