Automata for Infinite Argumentation Structures
  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.
