From Weighted Conditionals of Multilayer Perceptrons to Gradual Argumentation and Back

TL;DR

This paper explores the connection between weighted conditionals in neural networks and gradual argumentation semantics, proposing a unified fuzzy logic framework that extends to attack/support dynamics and defeasible reasoning.

Contribution

It introduces a novel fuzzy semantics linking multilayer perceptrons and argumentation, extending to attack/support relations and defeasible reasoning within a unified framework.

Findings

Establishes a relationship between neural networks and argumentation semantics.

Proposes a method to incorporate attack/support dynamics using fuzzy semantics.

Provides a framework for defeasible reasoning over weighted argumentation graphs.

Abstract

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.