HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Remarks on Gregory's ``Actually'' Operator

Abstract : In this paper we show that the classical modal technology of Sahlqvist formulas gives quick proofs of the completeness theorems in D. Gregory's `Completeness and Decidability results for some modal logics containing ``actually'' operators', Journal of Philosophical Logic 30(1):57-78, 2001, and vastly generalises them. As a corollary, interpolation theorems for the logics considered in Gregory's paper 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 Gregory's paper, 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.
Document type :
Journal articles
Complete list of metadata

https://hal.inria.fr/inria-00100891
Contributor : Publications Loria Connect in order to contact the contributor
Submitted on : Tuesday, September 26, 2006 - 2:52:42 PM
Last modification on : Friday, February 4, 2022 - 3:23:17 AM

Identifiers

  • HAL Id : inria-00100891, version 1

Collections

Citation

Patrick Blackburn, Maarten Marx. Remarks on Gregory's ``Actually'' Operator. Journal of Philosophical Logic, Springer Verlag, 2002, 31, pp.281-288. ⟨inria-00100891⟩

Share

Metrics

Record views

39