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Possibility and Dyadic Contingency
Journal of Logic, Language and Information ( IF 0.8 ) Pub Date : 2022-04-28 , DOI: 10.1007/s10849-022-09352-3
Claudio E. A. Pizzi 1
Affiliation  

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(\({\textsf{T}}\), A). In the second section it is proved that the deontic system KD is translationally equivalent to an axiomatic system of dyadic noncontingency named KDΔ2, and that the minimal system KΔ of monadic contingency is a fragment of KDΔ2. The last section suggests lines for further inquiries.



中文翻译:

可能性和二元偶然性

本文旨在发展这样一种观点,即通常用 Δ 表示的非偶然性标准算子是二元非偶然性 Δ(-, -) 的更一般算子的一个特例。这样的概念可以以不同的方式模态定义。论文中考察的是Δ (B, A) =  df ◊B ∧ (A ⥽ B ∨ A ⥽ ¬B),其中⥽代表严格蕴涵。二元偶然性 (B, A) 的算子被定义为Δ (B, A) 的否定。可能性 (◊A) 可以定义为Δ (A, A),必要性 (□A) 可以定义为∇ ( ¬A , ¬A),标准一元非偶然性 (ΔA) 可以定义为Δ ( \({\textsf{T} }\), 一种)。第二部分证明了道义系统KD平移等价于一个名为KDΔ2的二元非偶然性公理系统,并且一元偶然性的最小系统是KDΔ2的一个片段。最后一节建议进一步查询的线路。

更新日期:2022-04-29
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