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arXiv · 2208.01479

Interval-Dismantling for Lattices

Maximilian Felde·Maren Koyda
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Abstract

Dismantling allows for the removal of elements of a set, or in our case lattice, without disturbing the remaining structure. In this paper we have extended the notion of dismantling by single elements to the dismantling by intervals in a lattice. We utilize theory from Formal Concept Analysis (FCA) to show that lattices dismantled by intervals correspond to closed subrelations in the respective formal context, and that there exists a unique kernel with respect to dismantling by intervals. Furthermore, we show that dismantling intervals can be identified directly in the formal context utilizing a characterization via arrow relations and provide an algorithm to compute all dismantling intervals.

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Maximilian Felde, Maren Koyda. 2022-08-02. Interval-Dismantling for Lattices. https://doi.org/10.1016/j.ijar.2023.108931

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