Strong negation is definable in 2Int
Abstract
Abstract In intuitionistic logic, a formula is considered false when absurdity is derivable from it. Nelson’s paraconsistent logic $\text{N4}$ and Wansing’s bi-intuitionistic logic $\text{2Int}$ take two different approaches to introducing a more direct notion of falsity. $\text{N4}$ adds a strong negation connective to the language, which expresses that a formula is refutable, while $\text{2Int}$ formalizes proof and refutation as separate consequence relations, together with separate assumptions and counter-assumptions. This note shows that the strong negation from $\text{N4}$ is definable in $\text{2Int}$.
Fields of Study & Subjects
Computability
Logic
AI Algorithms
Reasoning
and Knowledge
Advanced Algebra and Logic
Publication details
- Journal / source
- Journal of Logic and Computation
- Volume
- 36
- Issue
- 6
- Publication date
- 24 June 2026
- Language
- EN