Together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that—similar to relatively pseudocomplemented lattices—these structures can serve as an algebraic semantics of certain intuitionistic logics. The aim of the present paper is to define congruences and filters in these structures, derive mutual relationships between them and describe basic properties of congruences in strongly sectionally pseudocomplemented posets. For the description of filters in both sectionally pseudocomplemented lattices and posets, we use the tools introduced by A. Ursini, i.e., ideal terms and the closedness with respect to them. It seems to be of some interest that a similar machinery can be applied also for strongly sectionally pseudocomplemented posets in spite of the fact that the corresponding ideal terms are not everywhere defined.

我们与 J. Paseka 一起引入了所谓的分段伪补格和偏序集，并阐明了它们在代数构造中的作用。我们相信，类似于相对伪补格，这些结构可以充当某些直觉逻辑的代数语义。本文的目的是定义这些结构中的同余和过滤器，推导它们之间的相互关系，并描述强分段伪补偏序集中同余的基本属性。为了描述分段伪补格和偏序集中的滤波器，我们使用 A. Ursini 引入的工具，即理想项和相对于它们的封闭性。似乎有些有趣的是，类似的机制也可以应用于强分段伪补偏序集，尽管相应的理想项并非到处都有定义。