ICCMA

International Competition on Computational Models of Argumentation

Competition Rules

The competition will be made of four different tracks, each of them divided into sub-tracks corresponding to various extension semantics. For each sub-track, between one and four 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 entities 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 in addition 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

• conflict-free (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 semi-stable 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 extensions. 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.

Assumption-based Argumentation

Now we present Assumption-based 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 (non-empty) set of assumptions
• ‾ is a mapping from assumptions to literals, that represents a notion of contrariness

A rule x₀ ← x₁,...,x_n is made of literals x₀, x₁,... x_n ∈ L, and n ≥ 0. A rule x₀ ← can be understood as a fact, or alternatively x₀ ← ⊤. We consider only flat ABA frameworks, i.e. ABA frameworks where there is no assumption in the head of a rule, which means no rule x₀ ← x₁,...,x_n such that x₀ is an assumption. A deduction for a literal x ∈ L, supported by X_L and X_R is a finite tree rooted in x, with nodes labeled by symbols in L (or ⊤), and such that

• each leaf is either a symbol in X_L or ⊤,
• for each non-leaf node, with label x', its children are x₁,...,x_n such that the rule x' ← x₁,...,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 Arg₁ = A₁ ⊢ x₁ and Arg₂ = A₂ ⊢ x₂, we say that Arg₁ attacks Arg₂ if x₁ is the contrary of some assumption in A₂. 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 A₁ attacks a set of assumptions A₂ if an argument supported by a subset of A₁ attacks an argument supported by a subset of A₂;
• A set of assumptions A₁ defends an assumption a if A₁ 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 Tasks

We introduce the four reasoning tasks of the competition:

CE-σ

Given an AF F = (A,R), give the number of σ-extensions of F.

SE-σ

Given an AF F = (A,R), give one σ-extensions of F.

DC-σ

Given an AF F = (A,R) and an argument a ∈ A, is a credulously accepted in F?

DS-σ

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 DC-σ and DS-σ.

Tracks

Static Abstract Argumentation

The Static Abstract Argumentation track is divided into six sub-tracks, corresponding to the following semantics: complete (co), preferred (pr), stable (st), semi-stable (sst), stage (stg) and ideal (id). For σ ∈ { co, pr, st, sst, stg}, the four problems CE-σ, SE-σ, DC-σ and DS-σ will be considered. For σ = id, only SE-σ and DS-σ will be considered (since CE-σ is always trivially 1, and DS-σ coincides with DC-σ).

Dynamic Abstract Argumentation

The Dynamic Abstract Argumentation track is divided into three sub-tracks, corresponding to the complete (co), preferred (pr) and stable (st) semantics. For each of them, we consider the dynamic version of the four problems CE-σ, SE-σ, DC-σ and DS-σ: 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 sub-tracks, corresponding to the complete (co), preferred (pr) and stable (st) semantics. Each sub-track is made of four reasoning tasks, namely CE-σ, SE-σ, DC-σ and DS-σ.

Approximate Algorithms

A track dedicated to approximate algorithms is included for the first time at ICCMA. For this exploratory track, we restrict the reasoning tasks to only two: the decision problems DC-σ and DS-σ, for five different sub-tracks: σ ∈ { co, pr, st, sst, stg }, as well as DS for the sub-track σ = id. We will evaluate the solvers with respect to their accuracy, i.e. the ratio of instances that are correctly solved. The main interest of approximate algorithms over exact algorithms is their (potentially) lower runtime. Thus, the timeout will be 60 seconds, contrary to the other tracks.

Solver Interface

See the Solver Requirements.

Scoring Rules

The scoring rules are different for exact algorithms (i.e. the tracks on static/dynamic abstract argumentation and structured argumentation) and approximate algorithms. Let us start with exact algorithms. For each sub-track:

• in case of any wrong result, the solver is excluded from the sub-track;
• for every correct answer within the runtime limit (600 seconds), the solver gets a score of 1; in case of timeout or non-parsable output, the score is 0;
• the cumulated runtime over the correctly solved instances is used for breaking ties.

For approximate algorithms, the scoring rule is slightly different. For each sub-track:

• for every correct answer within the runtime limit (60 seconds), the solver gets a score of 1;
• for every incorrect answer, timeout or non-parsable output, the score is 0;
• the cumulated runtime over the correctly solved instances is used for breaking ties.

References

• [Dung 95] P. M. Dung, On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n-Person Games. Artif. Intell. 77(2): 321-358 (1995)

• [Caminada et al 12] M. Caminada, W. Carnielli, P. Dunne, Semi-stable semantics. J. Log. Comput. 22(5): 1207-1254 (2012)

• [Verheij 96] B. Verheij, Two approaches to dialectical argumentation: admissible sets and argumentation stages. Proc. of NAIC'96: 357-368 (1996).

• [Dung et al 07] P. M. Dung, P. Mancarella, F. Toni, Computing ideal sceptical argumentation. Artif. Intell. 171(10-15): 642-674 (2007)

• [Bondarenko et al 97] A. Bondarenko, P. M. Dung, R. Kowalski, F. Toni, An Abstract, Argumentation-Theoretic Approach to Default Reasoning. Artif. Intell. 93: 63-101 (1997)

Last updated 22.10.2019, Matthias Thimm | Terms