Analytic Non-Labelled Proof-Systems for Hybrid Logic: Overview and a couple of striking facts

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Abstract

This paper is about non-labelled proof-systems for hybrid logic, that is, proof-systems where arbitrary formulas can occur, not just satisfaction statements. We give an overview of such proof-systems, focusing on analytic systems: Natural deduction systems, Gentzen sequent systems and tableau systems. We point out major results and we discuss a couple of striking facts, in particular that non-labelled hybrid-logical natural deduction systems are analytic, but this is not proved in the usual way via step-by-step normalization of derivations.
Original languageEnglish
JournalBulletin of the Section of Logic
Volume51
Issue number2
Pages (from-to)143-162
Number of pages20
ISSN0138-0680
DOIs
Publication statusPublished - Jun 2022

Keywords

  • Hybrid logic
  • Natural deduction systems
  • Sequent systems
  • Normalization
  • Cut-elimination
  • Analycity

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