# On the Usability of Probably Approximately Correct Implication Bases

arXiv: https://arxiv.org/abs/1701.00877 · HTML: https://mlsanity.com/paper/1701.00877/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2017.

## Built on by (most cited first, 2 of 2)

- [Towards Ordinal Data Science](https://mlsanity.com/paper/2307.09477/) (2023)
- [When Can a Machine Trust a Statute? A Survival Certificate for Machine-Extracted Legal Logic](https://mlsanity.com/paper/2609.01741/) (2026)

## Abstract (arXiv)

We revisit the notion of probably approximately correct implication bases from the literature and present a first formulation in the language of formal concept analysis, with the goal to investigate whether such bases represent a suitable substitute for exact implication bases in practical use-cases. To this end, we quantitatively examine the behavior of probably approximately correct implication bases on artificial and real-world data sets and compare their precision and recall with respect to their corresponding exact implication bases. Using a small example, we also provide qualitative insight that implications from probably approximately correct bases can still represent meaningful knowledge from a given data set.