Automata for Infinite Argumentation Structures
This work addresses the problem of modeling infinite argumentation processes in contexts like multi-agent negotiation and ambient intelligence, representing a novel method for a known bottleneck.
The paper tackles the limitation of finite structures in abstract argumentation frameworks by proposing a novel approach using deterministic finite automata and attack expressions to describe infinite argumentation frameworks, showing it can capture a large variety of infinite structures and that several computational problems remain decidable with provided algorithms.
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.