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Journal Articles Journal of Philosophical Logic Year : 2002

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.

Domains

Other [cs.OH]
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Dates and versions

inria-00100891 , version 1 (26-09-2006)

Identifiers

  • HAL Id : inria-00100891 , version 1

Cite

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