Notre Dame Journal of Formal Logic

First-Order Modal Logic with an 'Actually' Operator

Yannis Stephanou


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.

Article information

Notre Dame J. Formal Logic, Volume 46, Number 4 (2005), 381-405.

First available in Project Euclid: 12 December 2005

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Zentralblatt MATH identifier

Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}

actually operators first-order modal logic


Stephanou, Yannis. First-Order Modal Logic with an 'Actually' Operator. Notre Dame J. Formal Logic 46 (2005), no. 4, 381--405. doi:10.1305/ndjfl/1134397658.

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