Competition Rules
The competition will be made of three different
tracks, each of them divided into subtracks
corresponding to various extension semantics. For each
subtrack, four (or two, in the case of singlestatus
semantics) reasoning tasks must be solved. This page
describes these (sub)tracks and the reasoning tasks,
as well as the scoring rules.
Abstract Argumentation
We recall here the definition of Dung's Abstract
Argumentation Frameworks (AFs) [Dung 95], as well as extension semantics.
An AF is a directed graph F = (A,R) where A is a set of
abstract entites called arguments, and R ⊆ A
× A is the attack relation. For a,b ∈ A,
we say that a attacks b when (a,b) ∈ R. If b
attacks c, for some c ∈ A, then a defends c
against b. These concepts can be extended to sets of
arguments: S ⊆ A attacks (respectively defends) an
argument b ∈ A if there is some a ∈ S that attacks
(respectively defends) b. Now we can introduce basic
requirements that must be satisfied by a set of arguments in
order to be acceptable. A set S ⊆ A is
 conflictfree (S ∈ cf(F)) if S does not attack any of its
elements;
 admissible (S ∈ ad(F)) if S ∈ cf(F)
and S defends all its elements against all their attackers.
Finally, S⊕ = S ∪ { a ∈ A  S attacks a
} is called the
range of S.
From these basic concepts, several semantics can be
defined. A set S ⊆ A is
 a complete extension (S ∈ co(F)) if S
∈ ad(F) and S contains all the arguments that it defends;
 a preferred extension (S ∈ pr(F)) if S
∈ ad(F) and for every S' such that S ⊂ S', S'
∉ ad(F);
 a stable extension (S ∈ st(F)) if S ∈
cf(F) and S attacks each argument not in S;
 a semistable extension (S ∈ sst(F)) if S
∈ co(F) and for every S' such that S⊕ ⊂
S'⊕, S' ∉ co(F);
 a stage extension (S ∈ stg(F)) if S
∈ cf(F) and for every S' such that S⊕ ⊂
S'⊕, S' ∉ cf(F);
 an ideal extension (S ∈ id(F)) if S ∈
ad(F), S is included in every preferred extension, and there
is no S' ∈ ad(F) included in every preferred extension
such that S ⊂ S'.
Among these semantics only the stable semantics can produce no
extension. For the semantics except the ideal semantics,
there may be several extension. Only the ideal semantics
gives exactly one extension for any AF. See [Dung 95, Caminada et al 12, Verheij 96, Dung et al 07] for more details.
Assumptionbased Argumentation
Now we present Assumptionbased Argumentation (ABA) [Bondarenko et al 97] and
the corresponding semantics.
An ABA framework is a tuple F = (L,R,A,‾) where
 L is a set of literals
 R is a set of rules
 A ⊆ L is a (nonempty) set of assumptions
 ‾ is a mapping from assumptions to literals, that
represents a notion of contrariness
A rule x
_{0} ← x
_{1},...,x
_{n} is made of
literals x
_{0}, x
_{1},... x
_{n} ∈ L, and n
≥ 0. A rule x
_{0} ← can be understood as a
fact, or alternatively x
_{0} ← ⊤. A
deduction for a literal x ∈ L, supported by
X
_{L} and X
_{R} is a finite tree rooted in
x, with nodes labelled by symboles in L (or ⊤), and
such that
 each leaf is either a symbol in X_{L} or
⊤,
 for each nonleaf node, with label x', its children are
x_{1},...,x_{n} such that the rule x' ←
x_{1},...,x_{n} is in X_{R}.
Then, given a literal x ∈ L, an argument for x, supported
by the set of assumptions X
_{A}, is a deduction for
x supported by X
_{A} (and some rules X
_{R}).
This is denoted X
_{A} ⊢ x. Given two arguments
Arg
_{1} = A
_{1} ⊢ x
_{1} and
Arg
_{2} = A
_{2} ⊢ x
_{2}, we
say that Arg
_{1} attacks Arg
_{2} if
x
_{1} is the contrary of some assumption in
A
_{2}. Now, notions of attacks and defense between
sets of assumptions can be introduced, in order to define
extension semantics for ABA frameworks.
 A set of assumptions A_{1} attacks a set of
assumptions A_{2} if an argument supported by a
subset of A_{1} attacks an argument supported by a
subset of A_{2};
 A set of assumptions A_{1} defends an assumption
a if A_{1} attacks every set of assumption that
attacks a.
Then, extension semantics can be defined for an ABA framework.
In particular, given X
_{A} ⊆ A,
 X_{A} ∈ cf(F) if it does not attack any of
its elements;
 X_{A} ∈ ad(F) if X_{A} ∈ cf(F)
and X_{A} defends all its elements;
 X_{A} ∈ co(F) if X_{A} ∈ ad(F)
and X_{A} contains all the assumptions that it defends;
 X_{A} ∈ pr(F) if it is a ⊆maximal
admissible set of F;
 X_{A} ∈ st(F) if X_{A} ∈ cf(F)
and X_{A} attacks every assumption in A ∖ X_{A}.
Reasoning Tasts
We introduce the four reasoning tasks of the
competition:
 CEσ
 Given an AF F = (A,R), give the number of σextensions of F.
 SEσ
 Given an AF F = (A,R), give one σextensions of F.
 DCσ
 Given an AF F = (A,R) and an argument a ∈ A, is a
credulously accepted in F?
 DSσ
 Given an AF F = (A,R) and an argument a ∈ A, is a
skeptically accepted in F?
These problems can be equivalently defined for ABA
frameworks, considering F = (L,R,A,‾) instead of
F = (A,R), and an assumption instead of an argument
for DCσ and DSσ.
Tracks
Static Abstract Argumentation
The Static Abstract Argumentation track is divided into
six subtracks, corresponding to the following
semantics: complete (co), preferred (pr), stable (st),
semistable (sst), stage (stg) and ideal (id). For
σ ∈ { co, pr, st, sst, stg }, the
four problems CEσ, SEσ, DCσ and
DSσ will be considered. For σ = id, only
SEσ and DSσ will be considered (since
CEσ is always trivially 1, and DSσ
coincides with DCσ).
Dynamic Abstract Argumentation
The Dynamic Abstract Argumentation track is divided into
three subtracks, corresponding to the complete (co),
preferred (pr) and stable (st) semantics. For each of
them, we consider the dynamic version of the four
problems CEσ, SEσ, DCσ and
DSσ: the solver must solve the given problem for
an input AF, and then solving it again for a sequence of
updates of the AF. An update can be:
 the addition of an attack between two existing
arguments;
 the deletion of an attack between two existing
arguments;
 the addition of a new argument, as well as a set
of incident attacks;
 the deletion of an existing argument, as well as
all the incident attacks.
Structured Argumentation
The Structured Argumentation track is divided into
three subtracks, corresponding to the complete (co),
preferred (pr) and stable (st) semantics. Each subtrack
is made of four reasoning tasks, namely CEσ,
SEσ, DCσ and DSσ.
Solver Interface
To be announced...
Scoring Rules
To be announced...
References

[Dung 95] P. M. Dung, On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and nPerson Games. Artif. Intell. 77(2): 321358 (1995)

[Caminada et al 12] M. Caminada, W. Carnielli, P.
Dunne, Semistable semantics. J. Log. Comput. 22(5): 12071254 (2012)

[Verheij 96] B. Verheij, Two approaches to
dialectical argumentation: admissible sets and
argumentation stages. Proc. of NAIC'96: 357368 (1996).

[Dung et al 07] P. M. Dung, P. Mancarella, F. Toni, Computing ideal sceptical argumentation. Artif. Intell. 171(1015): 642674 (2007)

[Bondarenko et al 97] A. Bondarenko, P. M. Dung, R. Kowalski, F. Toni, An Abstract, ArgumentationTheoretic Approach to Default Reasoning. Artif. Intell. 93: 63101 (1997)