Remarks on Gregory's "actually" operator

Patrick Blackburn*, Maarten Marx

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


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.

Original languageEnglish
JournalJournal of Philosophical Logic
Issue number3
Pages (from-to)281-288
Number of pages8
Publication statusPublished - 2002
Externally publishedYes


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

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