First-Order Modal Logic with an 'Actually' Operator

Notre Dame Journal of Formal Logic 46 (4):381-405 (2005)
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Abstract

In this paper the language of first-order modal logic is enriched with an operator @ ('actually') such that, in any model, the evaluation of a formula @A at a possible world depends on the evaluation of A at the actual world. The models have world-variable domains. All the logics that are discussed extend the classical predicate calculus, with or without identity, and conform to the philosophical principle known as serious actualism. The basic logic relies on the system K, whereas others correspond to various properties that the actual world may have. All the logics are axiomatized

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References found in this work

Some theorems on the expressive limitations of modal languages.Harold T. Hodes - 1984 - Journal of Philosophical Logic 13 (1):13 - 26.
Remarks on Gregory's “actually” operator.Patrick Blackburn & Maarten Marx - 2002 - Journal of Philosophical Logic 31 (3):281-288.
Remarks on Gregory's “Actually” Operator.Blackburn Patrick & Marx Maarten - 2002 - Journal of Philosophical Logic 31 (3):281-288.
Investigations into Quantified Modal Logic.Yannis Stephanou - 2002 - Notre Dame Journal of Formal Logic 43 (4):193-220.

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