Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is currently lacking, and the theory of Nelson algebras remains largely unknown to most logicians. This paper aims to fill this gap by focussing on the essential developments in the field over the past two decades. Additionally, we explore generalisations of Nelson algebras, such as N4-lattices which correspond to the paraconsistent version of Nelson's logic, as well as their applications to other areas of interest to logicians, such as duality and rough set theory. A general representation theorem states that each Nelson algebra is isomorphic to a subalgebra of a rough set-based Nelson algebra induced by a quasiorder. Furthermore, a formula is a theorem of Nelson logic if and only if it is valid in every finite Nelson algebra induced by a quasiorder.

翻译：过去50年间，杰出学者们对Nelson代数进行了广泛研究，将其视为具有强否定的Nelson构造性逻辑的代数对应物。然而，尽管研究丰富，目前仍缺乏关于该主题的全面综述，大多数逻辑学者对Nelson代数理论仍知之甚少。本文通过聚焦该领域近二十年的重要进展，旨在填补这一空白。此外，我们探讨了Nelson代数的推广形式（例如对应于Nelson逻辑悖论版本的N4-格），以及它们在逻辑学者感兴趣的其他领域（如对偶性和粗糙集理论）中的应用。一个通用表示定理表明：每个Nelson代数都同构于由拟序诱导的基于粗糙集的Nelson代数的子代数。进一步地，一个公式是Nelson逻辑的定理当且仅当它在每个由拟序诱导的有限Nelson代数中有效。