# A framework for a modular multi-concept lexicographic closure semantics

arXiv: https://arxiv.org/abs/2009.00964 · HTML: https://mlsanity.com/paper/2009.00964/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2020.

## Built on by (most cited first, 5 of 5)

- [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)
- [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)
- [A framework for Conditional Reasoning in Answer Set Programming](https://mlsanity.com/paper/2506.03997/) (2025)

## Abstract (arXiv)

We define a modular multi-concept extension of the lexicographic closure semantics for defeasible description logics with typicality. The idea is that of distributing the defeasible properties of concepts into different modules, according to their subject, and of defining a notion of preference for each module based on the lexicographic closure semantics. The preferential semantics of the knowledge base can then be defined as a combination of the preferences of the single modules. The range of possibilities, from fine grained to coarse grained modules, provides a spectrum of alternative semantics.