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 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

• 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 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.

### 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,...,xn is made of literals x0, x1,... xn ∈ 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,...,xn such that x0 is an assumption. A deduction for a literal x ∈ L, supported by XL and XR 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 XL or ⊤,
• for each non-leaf node, with label x', its children are x1,...,xn such that the rule x' ← x1,...,xn is in XR.
Then, given a literal x ∈ L, an argument for x, supported by the set of assumptions XA, is a deduction for x supported by XA (and some rules XR). This is denoted XA ⊢ 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 XA ⊆ A,
• XA ∈ cf(F) if it does not attack any of its elements;
• XA ∈ ad(F) if XA ∈ cf(F) and XA defends all its elements;
• XA ∈ co(F) if XA ∈ ad(F) and XA contains all the assumptions that it defends;
• XA ∈ pr(F) if it is a ⊆-maximal admissible set of F;
• XA ∈ st(F) if XA ∈ cf(F) and XA attacks every assumption in A ∖ XA.

### Reasoning Tasts

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 one: SE-σ, for three different sub-tracks: σ ∈ { pr, sst, stg }. For these sub-tracks, we expect the solver to return one set of arguments, with the constraint that this set must be a subset of an actual σ-extension. The closer it is to an actual extension, the better is the score of the solver (see the scoring rules below for details).

### Solver Interface

To be announced...

### 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, 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 different. The expected output of the solvers is a set of arguments. An acceptable answer is then a subset of an actual σ-extension. The score of the solver depends on the distance between the output and the closest actual extension. If the output is an extension, it gets the maximal score of 1. Otherwise, the score decreases with the number of missing arguments. Outputs that are not subsets of actual extensions receive a score of 0.

### 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