# A Polynomial Time Subsumption Algorithm for Nominal Safe ELO_bot under Rational Closure

arXiv: https://arxiv.org/abs/1802.08201 · HTML: https://mlsanity.com/paper/1802.08201/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2018.

## Built on by (most cited first, 8 of 8)

- [A conditional, a fuzzy and a probabilistic interpretation of self-organising maps](https://mlsanity.com/paper/2103.06854/) (2021)
- [On the KLM properties of a fuzzy DL with Typicality](https://mlsanity.com/paper/2106.00390/) (2021)
- [Weighted Conditional EL{^}bot Knowledge Bases with Integer Weights: an ASP Approach](https://mlsanity.com/paper/2109.08286/) (2021)
- [From Weighted Conditionals of Multilayer Perceptrons to Gradual Argumentation and Back](https://mlsanity.com/paper/2110.03643/) (2021)
- [A preferential interpretation of MultiLayer Perceptrons in a conditional logic with typicality](https://mlsanity.com/paper/2305.00304/) (2023)
- [Reasoning on textitDL-Litecal R with Defeasibility in ASP](https://mlsanity.com/paper/2106.14801/) (2021)
- [A Rational Entailment for Expressive Description Logics via Description Logic Programs](https://mlsanity.com/paper/2107.06075/) (2021)
- [Semantic Bridges Between First Order c-Representations and Cost-Based Semantics: An Initial Perspective](https://mlsanity.com/paper/2510.00817/) (2025)

## Abstract (arXiv)

Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe ELO_bot, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe ELO_bot under RC that relies entirely on a series of classical, monotonic EL_bot subsumption tests. Therefore, any existing classical monotonic EL_bot reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability.