Abstract
In this paper we extend our first results concerning the characterisation of the graph structure of logic based argumentation graphs with two main classes of findings. First we provide full proofs for the structural results of argumentation graphs built over DatalogĀ± knowledge base composed of facts and negative constraints solely. Second, we also provide some structural properties for the general case of knowledge bases composed of facts, rules and negative constraints.
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Notes
- 1.
In the rest of the paper, and in order to simplify the notation, we omit cycles corresponding to singleton orbits.
- 2.
We say that a tuple of arguments \((a_1, \ldots , a_n)\) is a cycle if and only if \(a_1 \mathcal {C}a_2\), \(\ldots \), \(a_{n-1} \mathcal {C}a_n\) and \(a_n \mathcal {C}a_1\).
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Yun, B., Croitoru, M., Vesic, S., Bisquert, P. (2018). Graph Theoretical Properties of Logic Based Argumentation Frameworks: Proofs and General Results. In: Croitoru, M., Marquis, P., Rudolph, S., Stapleton, G. (eds) Graph Structures for Knowledge Representation and Reasoning. GKR 2017. Lecture Notes in Computer Science(), vol 10775. Springer, Cham. https://doi.org/10.1007/978-3-319-78102-0_7
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