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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.
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Submitted on : Tuesday, September 26, 2006 - 2:52:42 PM
Last modification on : Friday, February 26, 2021 - 3:28:03 PM


  • HAL Id : inria-00100891, version 1



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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