Possibility and Dyadic Contingency

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 (ΔA) as Δ(T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textsf{T}}$$\end{document}, A). In the second section it is proved that the deontic system KD is translationally equivalent to an axiomatic system of dyadic noncontingency named KDΔ2, and that the minimal system KΔ of monadic contingency is a fragment of KDΔ2. The last section suggests lines for further inquiries.