# From Weighted Conditionals of Multilayer Perceptrons to Gradual Argumentation and Back

arXiv: https://arxiv.org/abs/2110.03643 · HTML: https://mlsanity.com/paper/2110.03643/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 58 references that are in the map.
- First posted on arXiv 7 Oct 2021.

## Builds on (most cited first, 10 of 10)

- [Interpreting Neural Networks as Gradual Argumentation Frameworks (Including Proof Appendix)](https://mlsanity.com/paper/2012.05738/) (2020)
- [An ASP approach for reasoning in a concept-aware multipreferential lightweight DL](https://mlsanity.com/paper/2006.04387/) (2020)
- [Weighted defeasible knowledge bases and a multipreference semantics for a deep neural network model](https://mlsanity.com/paper/2012.13421/) (2020)
- [A Polynomial Time Subsumption Algorithm for Nominal Safe ELO_bot under Rational Closure](https://mlsanity.com/paper/1802.08201/) (2018)
- [On Rational Entailment for Propositional Typicality Logic](https://mlsanity.com/paper/1809.10946/) (2018)
- [On the Semantics of Abstract Argumentation Frameworks: A Logic Programming Approach](https://mlsanity.com/paper/2008.02550/) (2020)
- [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)
- [On a plausible concept-wise multipreference semantics and its relations with self-organising maps](https://mlsanity.com/paper/2008.13278/) (2020)
- [A framework for a modular multi-concept lexicographic closure semantics](https://mlsanity.com/paper/2009.00964/) (2020)

## Built on by (most cited first, 1 of 1)

- [An ASP approach for reasoning on neural networks under a finitely many-valued semantics for weighted conditional knowledge bases](https://mlsanity.com/paper/2202.01123/) (2022)

## Abstract (arXiv)

A fuzzy multipreference semantics has been recently proposed for weighted conditional knowledge bases, and used to develop a logical semantics for Multilayer Perceptrons, by regarding a deep neural network (after training) as a weighted conditional knowledge base. This semantics, in its different variants, suggests some gradual argumentation semantics, which are related to the family of the gradual semantics studied by Amgoud and Doder. The relationships between weighted conditional knowledge bases and MLPs extend to the proposed gradual semantics to capture the stationary states of MPs, in agreement with previous results on the relationship between argumentation frameworks and neural networks. The paper also suggests a simple way to extend the proposed semantics to deal attacks/supports by a boolean combination of arguments, based on the fuzzy semantics of weighted conditionals, as well as an approach for defeasible reasoning over a weighted argumentation graph, building on the proposed gradual semantics.