Remarks on Gregory's "actually" operator

Patrick Blackburn*, Maarten Marx

*Corresponding author

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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.
TidsskriftJournal of Philosophical Logic
Udgave nummer3
Sider (fra-til)281-288
Antal sider8
StatusUdgivet - 2002
Udgivet eksterntJa


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

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