In this paper, we build a logic which is named N-sequent calculus. Based on this logic, we provide two kinds of logical representations of Lawson compact algebraic L-domains: one in terms of logical algebras and the other in terms of logical syntax.

The first representation takes the corresponding logical algebras as research objects. The use of prime filters achieves the connection between our logic and Lawson compact algebraic L-domains. This approach is inspired by Abramsky's SFP domain logic and the disjunctive propositional logic on algebraic L-domains introduced by Yixiang Chen and Achim Jung. However, there are essential differences between them at the morphisms part. For the second representation, we directly adopt N-sequent calculi themselves as objects instead of the logical algebras. Then we establish the category of N-sequent calculi with consequence relations equivalent to that of Lawson compact algebraic L-domains with Scott continuous maps. This demonstrates the capability of the syntax of the logic in representing domains.

在本文中，我们建立了一个称为N次演算的逻辑。基于这种逻辑，我们提供了Lawson紧凑代数L域的两种逻辑表示形式：一种是逻辑代数，另一种是逻辑句法。

第一种表示形式将相应的逻辑代数作为研究对象。质数滤波器的使用实现了我们的逻辑与Lawson紧凑代数L域之间的联系。这种方法的灵感来自于Abramsky的SFP域逻辑以及由Chen Yixiang和Achim Jung提出的关于代数L域的析取命题逻辑。但是，在射态部分它们之间有本质的区别。对于第二种表示形式，我们直接采用N次运算本身作为对象，而不是逻辑代数。然后，我们建立具有与Scott连续映射的Lawson紧代数L域的后果关系相等的后果关系的N后续计算类别。这证明了逻辑语法在表示域中的能力。