Many-valued Argumentation, Conditionals and a Probabilistic Semantics for Gradual Argumentation

TL;DR

This paper introduces a comprehensive many-valued framework for gradual argumentation, enabling conditional reasoning and boolean combinations, supported by an Answer Set Programming implementation and a probabilistic semantics extension.

Contribution

It presents a novel many-valued preferential interpretation for gradual argumentation, integrating conditional reasoning, boolean combinations, and probabilistic semantics.

Findings

Developed a finitely-valued argumentation semantics using Answer Set Programming

Proposed a probabilistic semantics for gradual argumentation

Enabled conditional reasoning over weighted argumentation graphs

Abstract

In this paper we propose a general approach to define a many-valued preferential interpretation of gradual argumentation semantics. The approach allows for conditional reasoning over arguments and boolean combination of arguments, with respect to a class of gradual semantics, through the verification of graded (strict or defeasible) implications over a preferential interpretation. As a proof of concept, in the finitely-valued case, an Answer set Programming approach is proposed for conditional reasoning in a many-valued argumentation semantics of weighted argumentation graphs. The paper also develops and discusses a probabilistic semantics for gradual argumentation, which builds on the many-valued conditional semantics.