Possibility and Dyadic Contingency

• Published in: Journal of logic, language, and information Vol. 31; no. 3; pp. 451 - 463
• Main Author: Pizzi, Claudio E. A.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.09.2022
• Subjects: Education; Information Systems Applications (incl.Internet); Logic; Philosophy; Semantics; Necessity; Possibility; Noncontingency; Contingency
• ISSN: 0925-8531; 1572-9583
• DOI: 10.1007/s10849-022-09352-3

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 ( 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.