Remarks on Gregory's ``Actually'' Operator

Patrick Blackburn 1 Maarten Marx 2
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.
Type de document :
Article dans une revue
Journal of Philosophical Logic, Springer Verlag, 2002, 31, pp.281-288
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Soumis le : mardi 26 septembre 2006 - 14:52:42
Dernière modification le : jeudi 11 janvier 2018 - 06:19:48


  • 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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