# Remarks on Gregory's Actually'' Operator

1 LANGUE ET DIALOGUE - Human-machine dialogue with a significant language component
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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.
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Journal articles
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https://hal.inria.fr/inria-00100891
Contributor : Publications Loria <>
Submitted on : Tuesday, September 26, 2006 - 2:52:42 PM
Last modification on : Friday, February 26, 2021 - 3:28:03 PM

### Identifiers

• HAL Id : inria-00100891, version 1

### Citation

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

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