Logica Universalis 7 (1):113-123 (2013)

Claudio Pizzi
Università degli Studi di Siena
In the first part of the paper it is proved that there exists a one–one mapping between a minimal contingential logic extended with a suitable axiom for a propositional constant τ, named KΔτw, and a logic of necessity ${K\square \tau{w}}$ whose language contains ${\square}$ and τ. The form of the proposed translation aims at giving a solution to a problem which was left open in a preceding paper. It is then shown that the presence of τ in the language of KΔτw allows for the definition, in terms of the non-contingency operator Δ, not only of ${\square}$ but of a second necessity operator O. It is observed that this fact opens the road to an investigation of the τ-free multimodal fragments of KΔτw
Keywords Contingency  necessity  propositional constants  bimodal logics
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DOI 10.1007/s11787-012-0071-8
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References found in this work BETA

Relative Necessity.Timothy Smiley - 1963 - Journal of Symbolic Logic 28 (2):113-134.
Minimal Non-Contingency Logic.Steven T. Kuhn - 1995 - Notre Dame Journal of Formal Logic 36 (2):230-234.
The Logic of Non-Contingency.I. L. Humberstone - 1995 - Notre Dame Journal of Formal Logic 36 (2):214-229.
Completeness and Definability in the Logic of Noncontingency.Evgeni E. Zolin - 1999 - Notre Dame Journal of Formal Logic 40 (4):533-547.

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Logical Relations.Lloyd Humberstone - 2013 - Philosophical Perspectives 27 (1):175-230.

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