A series of representation theorems (some of which discovered very recently) present an alternative view of many classes of algebras related to non-classical logics (e.g. bilattices, semi-De Morgan, Nelson and quasi-Nelson algebras) as two-sorted algebras in the sense of many-sorted universal algebra. In all the above-mentioned examples, we are in fact dealing with a pair of lattices related by two meet-preserving maps. We use this insight to develop a Priestley-style duality for such structures, mainly building on the duality for meet-semilattices of G. Bezhanishvili and R. Jansana. Our approach simplifies all the existing dualities for these algebras and is applicable more generally; in particular, we show how it specialises to the class of quasi-Nelson algebras, which has not yet been studied from a duality point of view.

一系列表示定理（其中一些是最近才发现的）提出了与非经典逻辑有关的许多代数类（例如，双性，半德摩根，尼尔森和拟尼尔森代数）的另一种观点，它们是两类代数。多种通用代数的意义。在所有上述示例中，我们实际上是在处理由两个满足保留映射关系的一对晶格。我们利用这种洞察力为此类结构开发Priestley风格的对偶性，主要是在G. Bezhanishvili和R. Jansana的满足半指对偶性的基础上。我们的方法简化了这些代数的所有现有对偶关系，并且可以更广泛地应用。特别是，我们展示了它如何专门用于拟尼尔森代数，这尚未从二元性的角度进行研究。