# PN-OWL: A Two Stage Algorithm to Learn Fuzzy Concept Inclusions from OWL Ontologies

arXiv: https://arxiv.org/abs/2303.07192 · HTML: https://mlsanity.com/paper/2303.07192/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 109 references that are in the map.
- First posted on arXiv 1 Mar 2023.

## Builds on (most cited first, 4 of 4)

- [EMBER: An Open Dataset for Training Static PE Malware Machine Learning Models](https://mlsanity.com/paper/1804.04637/) (2018)
- [The DL-Lite Family and Relations](https://mlsanity.com/paper/1401.3487/) (2014)
- [Fuzzy OWL-BOOST: Learning Fuzzy Concept Inclusions via Real-Valued Boosting](https://mlsanity.com/paper/2008.05297/) (2020)
- [Knowledge-Based Dataset for Training PE Malware Detection Models](https://mlsanity.com/paper/2301.00153/) (2022)

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

- [Fuzzy Quantification over OWL Ontologies and Knowledge Graphs](https://mlsanity.com/paper/2606.25778/) (2026)
- [A Fuzzy Rule-based Neuro-Symbolic Approach for Pipe Severity Prediction in Sewer Networks](https://mlsanity.com/paper/2607.28481/) (2026)

## Abstract (arXiv)

OWL ontologies are a quite popular way to describe structured knowledge in terms of classes, relations among classes and class instances. In this paper, given a target class T of an OWL ontology, with a focus on ontologies with real- and boolean-valued data properties, we address the problem of learning graded fuzzy concept inclusion axioms with the aim of describing enough conditions for being an individual classified as instance of the class T. To do so, we present PN-OWL that is a two-stage learning algorithm made of a P-stage and an N-stage. Roughly, in the P-stage the algorithm tries to cover as many positive examples as possible (increase recall), without compromising too much precision, while in the N-stage, the algorithm tries to rule out as many false positives, covered by the P-stage, as possible. PN-OWL then aggregates the fuzzy inclusion axioms learnt at the P-stage and the N-stage by combining them via aggregation functions to allow for a final decision whether an individual is instance of T or not. We also illustrate its effectiveness by means of an experimentation. An interesting feature is that fuzzy datatypes are built automatically, the learnt fuzzy concept inclusions can be represented directly into Fuzzy OWL 2 and, thus, any Fuzzy OWL 2 reasoner can then be used to automatically determine/classify (and to which degree) whether an individual belongs to the target class T or not.