Automata for Infinite Argumentation Structures

TL;DR

This paper introduces a novel formalism using automata and formal language theory to model and analyze infinite argumentation frameworks, extending the finite case to infinite structures with practical decision procedures.

Contribution

It proposes a new automata-based approach for describing infinite argumentation frameworks, enabling analysis of infinite structures with desirable properties and decision algorithms.

Findings

The approach captures a wide range of infinite afs, including key examples from literature.

Decision problems in finite afs are extended to infinite afs with polynomial-time algorithms.

The method is effective for finitary afs, providing additional theoretical insights.

Abstract

The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this limitation, in this paper we propose a novel approach for describing infinite afs using tools from formal language theory. In particular, the possibly infinite set of arguments is specified through the language recognized by a deterministic finite automaton while a suitable formalism, called attack expression, is introduced to describe the relation of attack between arguments. The proposed approach is shown to satisfy some desirable properties which can not be achieved through other "naive" uses of formal languages. In particular, the approach is shown to be expressive enough to capture (besides any arbitrary finite structure) a large variety of infinite afs including two major examples from previous literature and two sample cases from the domains of multi-agent negotiation and ambient intelligence. On the computational side, we show that several decision and construction problems which are known to be polynomial time solvable in finite afs are decidable in the context of the proposed formalism and we provide the relevant algorithms. Moreover we obtain additional results concerning the case of finitary afs.