Abstract
We propose a novel approach to logic-based learning which generates assumption-based argumentation (ABA) frameworks from positive and negative examples, using a given background knowledge. These ABA frameworks can be mapped onto logic programs with negation as failure that may be non-stratified. Whereas existing argumentation-based methods learn exceptions to general rules by interpreting the exceptions as rebuttal attacks, our approach interprets them as undercutting attacks. Our learning technique is based on the use of transformation rules, including some adapted from logic program transformation rules (notably folding) as well as others, such as rote learning and assumption introduction. We present a general strategy that applies the transformation rules in a suitable order to learn stratified frameworks, and we also propose a variant that handles the non-stratified case. We illustrate the benefits of our approach with a number of examples, which show that, on one hand, we are able to easily reconstruct other logic-based learning approaches and, on the other hand, we can work out in a very simple and natural way problems that seem to be hard for existing techniques.
ILP 2022, 31st International Conference on Inductive Logic Programming, Cumberland Lodge, Windsor, UK.
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Notes
- 1.
The non-emptiness requirement can always be satisfied by including in \(\mathcal {A}\) a bogus assumption, with its own contrary, neither occurring elsewhere in the ABA framework. For conciseness, we will not write this assumption and its contrary explicitly.
- 2.
The other (ground) arguments are \(\{a(1)\} \vdash _{\{\rho _1(1)\}} p(1)\), \(\{a(2)\} \vdash _{\{\rho _1(2)\}} p(2)\), \(\{b(2)\} \vdash _{\{\rho _2(2)\}} q(2)\), \(\{a(2)\} \vdash _{\emptyset } a(2)\), \(\{b(1)\} \vdash _{\emptyset } b(1)\), and \(\{b(2)\} \vdash _{\emptyset } b(2)\).
- 3.
- 4.
The correspondence also holds under other semantics, omitted here for simplicity.
- 5.
We use the same notation for ABA rules and logic programs as, indeed, logic programming is an instance of ABAÂ [BDKT97].
- 6.
In fact the Dimopoulos-Kakas algorithm is just sketched and we have conjectured what we believe to be a reasonable result of this learning step.
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Acknowledgements
We thank the anonymous reviewers for useful comments. We also thank Mark Law for advice on the ILASP system. F. Toni was partially funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 101020934) and by J.P. Morgan and the Royal Academy of Engineering under the Research Chairs and Senior Research Fellowships scheme. M. Proietti is a member of the INdAM-GNCS research group.
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Proietti, M., Toni, F. (2024). Learning Assumption-Based Argumentation Frameworks. In: Muggleton, S.H., Tamaddoni-Nezhad, A. (eds) Inductive Logic Programming. ILP 2022. Lecture Notes in Computer Science(), vol 13779. Springer, Cham. https://doi.org/10.1007/978-3-031-55630-2_8
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