We study the computational complexity of the universal and quasi-equational theories of classes of bounded distributive lattices with a negation operation, i.e., a unary operation satisfying a subset of the properties of the Boolean negation. The upper bounds are obtained through the use of partial algebras. The lower bounds are either inherited from the equational theory of bounded distributive lattices or obtained through a reduction of a global satisfiability problem for a suitable system of propositional modal logic.

中文翻译：

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带负数的有界分布格的计算复杂度

我们用否定运算，即满足布尔否定性质的子集的一元运算，研究了有界分布格的类的通用和准方程理论的计算复杂性。上限是通过使用部分代数获得的。下限要么从有界分布格的方程理论中继承，要么通过减少适用于命题模态逻辑系统的全局可满足性问题来获得。