Discussion Graph Semantics of First-Order Logic with Equality for Reasoning about Discussion and Argumentation

TL;DR

This paper introduces a formal discussion-graph semantics for first-order logic with equality, enabling advanced reasoning about discussion and argumentation in AI, and generalizes existing frameworks to handle equivalence among nodes.

Contribution

It formulates a novel discussion-graph semantics for first-order logic with equality and extends Dung's argumentation framework to include equivalent nodes, connecting these concepts through first-order characterisability.

Findings

Formal discussion-graph semantics for first-order logic with equality

Generalization of Dung's extensions to equivalent nodes

First-order characterisability of all extensions and acceptability semantics

Abstract

We make three contributions. First, we formulate a discussion-graph semantics for first-order logic with equality, enabling reasoning about discussion and argumentation in AI more generally than before. This addresses the current lack of a formal reasoning framework capable of handling diverse discussion and argumentation models. Second, we generalise Dung's notion of extensions to cases where two or more graph nodes in an argumentation framework are equivalent. Third, we connect these two contributions by showing that the generalised extensions are first-order characterisable within the proposed discussion-graph semantics. Propositional characterisability of all Dung's extensions is an immediate consequence. We furthermore show that the set of all generalised extensions (acceptability semantics), too, are first-order characterisable. Propositional characterisability of all Dung's acceptability semantics is an immediate consequence.