Termination for hybrid tableaus

Thomas Bolander*, Patrick Blackburn

*Corresponding author

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review


This article extends and improves work on tableau-based decision methods for hybrid logic by Bolander and Braüner. Their paper gives tableau-based decision procedures for basic hybrid logic (with unary modalities) and the basic logic extended with the global modality. All their proof procedures make use of loop-checks to ensure termination. Here we take a closer look at termination for hybrid tableaus. We cover both types of system used in hybrid logic: prefixed tableaus and internalized tableaus. We first treat prefixed tableaus. We prove a termination result for the basic language (with n-ary operators) that does not involve loop-checks. We then successively add the global modality and n-ary inverse modalities, show why various different types of loop-check are required in these cases, and then re-prove termination. Following this we consider internalized tableaus. At first sight, such systems seem to be more complex. However, we define a internalized system which terminates without loop-checks. It is simpler than previously known internalized systems (all of which require loop-checks to terminate) and simpler than our prefix systems (no non-local side conditions on rules are required).
TidsskriftJournal of Logic and Computation
Udgave nummer3
Sider (fra-til)517-554
Antal sider38
StatusUdgivet - jun. 2007
Udgivet eksterntJa


  • Decision procedures
  • Hybrid logic
  • Loop-checks
  • Modal logic
  • Tableau systems

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