Journal of Philosophical Logic 31 (3):281-288 (2002)

Patrick Blackburn
Roskilde University
In this note we show that the classical modal technology of Sahlqvist formulas gives quick proofs of the completeness theorems in [8] (D. Gregory, Completeness and decidability results for some propositional modal logics containing "actually" operators, Journal of Philosophical Logic 30(1): 57-78, 2001) and vastly generalizes them. Moreover, as a corollary, interpolation theorems for the logics considered in [8] 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 [8], 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
Keywords modal logic  “actually” operators  Sahlqvist theory  Arthur Prior  hybrid logic  nominals
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Reprint years 2004
DOI 10.1023/A:1015726824270
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An Approach to Tense Logic.R. A. Bull - 1970 - Theoria 36 (3):282-300.

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Two-Dimensional Tableaux.David Gilbert - 2016 - Australasian Journal of Logic 13 (7).
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Free Choiceness and Non-Individuation.Jacques Jayez & Lucia M. Tovena - 2005 - Linguistics and Philosophy 28 (1):1 - 71.

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