Chapter 1
Assumption-Based Argumentation
Phan Minh Dung, Robert A. Kowalski, and Francesca Toni
1.1 Introduction
Assumption-Based Argumentation (ABA) [4, 3, 27, 9, 12, 20, 22] was developed,
starting in the 90s, as a computational framework to reconcile and generalise most
existing approaches to default reasoning [24, 25, 4, 3, 27, 26]. ABA was inspired
by Dung’s preferred extension semantics for logic programming [10, 7], with its di-
alectical interpretation of the acceptability of negation-as-failure assumptions based
on the notion of “no-evidence-to-the-contrary” [10, 7], by the Kakas, Kowalski and
Toni interpretation of the preferred extension semantics in argumentation-theoretic
terms [24, 25], and by Dung’s abstract argumentation (AA) [6, 8].
Because ABA is an instance of AA, all semantic notions for determining the
“acceptability” of arguments in AA also apply to arguments in ABA. Moreover,
like AA, ABA is a general-purpose argumentation framework that can be instan-
tiated to support various applications and specialised frameworks, including: most
default reasoning frameworks [4, 3, 27, 26] and problems in legal reasoning [27, 13],
game-theory [8], practical reasoning and decision-theory [33, 29, 15, 28, 14]. How-
ever, whereas in AA arguments and attacks between arguments are abstract and
primitive, in ABA arguments are deductions (using inference rules in an underly-
ing logic) supported by assumptions. An attack by one argument against another is
a deduction by the first argument of the contrary of an assumption supporting the
second argument.
Differently from a number of existing approaches to non-abstract argumentation
(e.g. argumentation based on classical logic [2] and DeLP [23]) ABA does not have
explicit rebuttals and does not impose the restriction that arguments have consistent
and minimal supports. However, to a large extent, rebuttals can be obtained “for
Phan Minh Dung
Asian Institute of Technology, Thailand, e-mail: dung@cs.ait.ac.th
Robert A. Kowalski, Francesca Toni
Imperial College London, UK, e-mail: {rak,ft}@doc.ic.ac.uk
1

2 Phan Minh Dung, Robert A. Kowalski, and Francesca Toni
free” [27, 9, 33]. Moreover, ABA arguments are guaranteed to be “relevant” and
largely consistent [34].
ABA is equipped with a computational machinery (in the form of dispute deriva-
tions [9, 12, 19, 20, 22]) to determine the acceptability of claims by building and
exploring a dialectical structure of a proponent’s argument for a claim, an oppo-
nent’s counterarguments attacking the argument, the proponent’s arguments attack-
ing all the opponents’ counterarguments, and so on. This computation style, which
has its roots in logic programming, has several advantages over other computational
mechanisms for argumentation. The advantages are due mainly to the fine level of
granularity afforded by interleaving the construction of arguments and determining
their “acceptability”.
The chapter is organised as follows. In Sections 1.2 and 1.3 we define the ABA
notions of argument and attack (respectively). In Section 1.4, we define “acceptabil-
ity” of sets of arguments, focusing on admissible and grounded sets of arguments.
In Section 1.5 we present the computational machinery for ABA. In Section 1.6 we
outline some applications of ABA. In Section 1.7 we conclude.
1.2 Arguments in ABA
ABA frameworks [3, 9, 12] can be defined for any logic specified by means of
inference rules, by identifying sentences in the underlying language that can be
treated as assumptions (see Section 1.3 for a formal definition of ABA frameworks).
Intuitively, arguments are “deductions” of a conclusion (or claim) supported by a set
of assumptions.
The inference rules may be domain-specific or domain-independent, and may
represent, for example, causal information, argument schemes, or laws and regu-
lations. Assumptions are sentences in the language that are open to challenge, for
example uncertain beliefs (“it will rain”), unsupported beliefs (“I believe X”), or
decisions (“perform action A”). Typically, assumptions can occur as premises of in-
ference rules, but not as conclusions. ABA frameworks, such as logic programming
and default logic, that have this feature are said to be flat [3]. We will focus solely
on flat ABA frameworks. Examples of non-flat frameworks can be found in [3].
As an example, consider the following simplification of the argument scheme
from expert opinion [37]:
Major premise: Source E is an expert about A.
Minor premise: E asserts that A is true.
Conclusion: A may plausibly be taken as true.
This can be represented in ABA by a (domain-independent) inference rule: 1
1 In this chapter, we use inference rule schemata, with variables starting with capital letters, to stand
for the set of all instances obtained by instantiating the variables so that the resulting premises and
conclusions are sentences of the underlying language. For simplicity, we omit the formal definition
of the language underlying our examples.