Abstract Argumentation Solving Graph Dataset

This repository contains a dataset of argumentation frameworks that includes enumerations of sets of extensions for each framework.

Argumentation Frameworks

An argumentation framework is a pair AF = (A, R), where A is a set of arguments and R is a binary relation over A that represents the attack relation.

A set S ⊆ A is conflict-free iff there are no attacking argument in S, and an argument a is defended by S iff any argument that attacks a is attacked by an argument in S. A set S is admissible iff it is conflict-free and defends all its arguments. Then, for a set E ⊆ A:

1. E is a complete extension (denoted CO) iff it is admissible any argument defended by E is in E,
2. E is the single, unique grounded extension (denoted GR) iff it is the smallest complete extension (w.r.t. set inclusion),
3. E is a preferred extension (denoted PR) iff it is a maximal complete extension (w.r.t. set inclusion),
4. E is a stable extension (denoted ST) iff it is a complete extension that attacks all arguments not in E,
5. E is a semi-stable extension (denoted SST) iff it is a complete extension that maximises the union of its members and the arguments its members attack, and
6. E is a stage extension (denoted STG) iff it is a complete extension that minimises the union of its members and the arguments its members attack.

Denote the set of all σ-extensions (where σ is one of the above semantics) as E_σ. An argument is credulously acceptable w.r.t. AF and σ iff it is in at least one σ-extension E ∈ E_σ, and it is sceptically acceptable iff it is in all σ-extensions E ∈ E_σ.

Dataset Details

The data is derived from the International Competition on Computational Models of Argumentation from the ICCMA 2017 benchmark datasets.

Solving Methodology

Each framework was read in .tgf format and translated into an .apx format using the store_af.py script. The .apx format is a simple text-based format that lists the arguments and attacks in the framework for input into an answer set programming solver. The .apx files were then solved using the ASPARTIX implementations of argumentation solving and the clingo answer-set programming solver, using the single_solve.py script.

Data Format

Each framework is stored in Python dictionary with the following keys, this is based on the pytorch_geometric data format.

• x: node feature matrix with shape (|A|, 1) consisting of unique integer identifiers for each argument (type torch.float32).
• edge_index: the relation R encoded in COO format with shape (2, |R|) and type torch.long.
• extensions: a dictionary mapping keys σ ∈ {"CO", "GR", "PR", "ST", "SST", "STG"} to binary tensors with shape (|E_σ|, |A|) and type torch.long.

For example:

{
    "x": torch.tensor([[0], [1], [2], [3]]),
    "edge_index": torch.tensor([[0, 1, 1, 2], [1, 2, 3, 3]]),
    "extensions": {
        "GR": torch.tensor([[1, 0, 1, 0]]),
        # ...
    }
}

Acknowledgements and License

The code is authored by Alex Jackson and is licensed under the MIT License.

This work was supported by UK Research and Innovation [grant number EP/S023356/1], in the UKRI Centre for Doctoral Training in Safe and Trusted Artificial Intelligence (www.safeandtrustedai.org).

In addition:

• The source data was provided as part of the International Competition on Computational Models of Argumentation.
• The ASPARTIX implementations of argumentation solving were created by the Database and Artificial Intelligence Group at the Vienna University of Technology.
• The clingo answer-set programming solver was created by the Potassco project.