## Computing with Infinite Argumentation Frameworks: the Case of AFRAs

### P. Baroni, F. Cerutti, P.E. Dunne, M. Giacomin

### In S. Modgil, N. Oren, F. Toni (Eds.), Theory and Applications of Formal
Argumentation - TAFA 2011 Revised Selected Papers, LNAI 7132, Springer, 2012,
197-214

###

### Abstract

In recent years a large corpus of studies has arisen from Dung’s seminal
abstract model of argumentation, including several extensions aimed at
increasing its expressiveness. Most of these works focus on the case of finite
argumentation frameworks, leaving the potential practical applications of
infinite frameworks largely unexplored. In the context of a recently proposed
extension of Dung’s framework called AFRA (Argumentation Framework with
Recursive Attacks), this paper makes a first step to fill this gap. It is shown
that, under some reasonable restrictions, infinite frameworks admit a compact
finite specification and that, on this basis, computational problems which are
tractable for finite frameworks may preserve the same property in the infinite
case. In particular we provide a polynomial-time algorithm to compute the finite
representation of the (possibly infinite) grounded extension of an AFRA with
infinite attacks. An example concerning the representation of a moral dilemma is
introduced to illustrate and instantiate the proposal and gives a preliminary
idea of its potential applicability.

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