## Notre Dame Journal of Formal Logic

### First-Order Modal Logic with an 'Actually' Operator

Yannis Stephanou

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 12 December 2005

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1134397658

Digital Object Identifier
doi:10.1305/ndjfl/1134397658

Mathematical Reviews number (MathSciNet)
MR2183050

Zentralblatt MATH identifier
1092.03010

#### Citation

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. https://projecteuclid.org/euclid.ndjfl/1134397658

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