Remarks on Gregory's "actually" operator

Patrick Blackburn*, Maarten Marx

*Corresponding author

Publikation: Bidrag til tidsskriftTidsskriftartikelpeer review

Abstract

In this note we show that the classical modal technology of Sahlqvist formulas gives quick proofs of the completeness theorems in [8] (D. Gregory, Completeness and decidability results for some propositional modal logics containing “actually” operators, Journal of Philosophical Logic 30(1): 57–78, 2001) and vastly generalizes them. Moreover, as a corollary, interpolation theorems for the logics considered in [8] are obtained. We then compare Gregory's modal language enriched with an “actually” operator with the work of Arthur Prior now known under the name of hybrid logic. This analysis relates the “actually” axioms to standard hybrid axioms, yields the decidability results in [8], and provides a number of complexity results. Finally, we use a bisimulation argument to show that the hybrid language is strictly more expressive than Gregory's language.
OriginalsprogEngelsk
TidsskriftJournal of Philosophical Logic
Vol/bind31
Udgave nummer3
Sider (fra-til)281-288
Antal sider8
ISSN0022-3611
DOI
StatusUdgivet - 2002
Udgivet eksterntJa

Emneord

  • "Actually" operators
  • Arthur Prior
  • Hybrid logic
  • Modal logic
  • Nominals
  • Sahlqvist theory

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