Possibility and Dyadic Contingency

Journal of Logic, Language and Information 31 (3):451-463 (2022)
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Abstract

The paper aims at developing the idea that the standard operator of noncontingency, usually symbolized by Δ, is a special case of a more general operator of dyadic noncontingency Δ(−, −). Such a notion may be modally defined in different ways. The one examined in the paper is __Δ__(B, A) = df ◊B ∧ (A ⥽ B ∨ A ⥽ ¬B), where ⥽ stands for strict implication. The operator of dyadic contingency __∇__(B, A) is defined as the negation of __Δ__(B, A). Possibility (◊A) may be then defined as __Δ__(A, A), necessity (□A) as __∇__(¬A, ¬A) and standard monadic noncontingency (__Δ__A) as __Δ__( \({\textsf{T}}\), A). In the second section it is proved that the deontic system KD is translationally equivalent to an axiomatic system of dyadic noncontingency named KDΔ 2, and that the minimal system KΔ of monadic contingency is a fragment of KDΔ 2. The last section suggests lines for further inquiries.

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Citations of this work

Some Notes on Dyadic Contingency.Jie Fan - 2023 - Journal of Logic, Language and Information 32 (2):209-217.

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References found in this work

The Logic of Non-contingency.I. L. Humberstone - 1995 - Notre Dame Journal of Formal Logic 36 (2):214-229.
Synonymous logics.Francis Jeffry Pelletier & Alasdair Urquhart - 2003 - Journal of Philosophical Logic 32 (3):259-285.
Minimal Non-contingency Logic.Steven T. Kuhn - 1995 - Notre Dame Journal of Formal Logic 36 (2):230-234.
Completeness and Definability in the Logic of Noncontingency.Evgeni E. Zolin - 1999 - Notre Dame Journal of Formal Logic 40 (4):533-547.
Necessity and contingency.M. J. Cresswell - 1988 - Studia Logica 47 (2):145 - 149.

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