Abstract
Many systems of structured argumentation explicitly require that the facts and rules that make up the argument for a conclusion be the minimal set required to derive the conclusion. \(\textsc {aspic}^{\mathsf {+}}\) does not place such a requirement on arguments, instead requiring that every rule and fact that are part of an argument be used in its construction. Thus \(\textsc {aspic}^{\mathsf {+}}\) arguments are minimal in the sense that removing any element of the argument would lead to a structure that is not an argument. In this paper we discuss these two types of minimality and show how the first kind of minimality can, if desired, be recovered in \(\textsc {aspic}^{\mathsf {+}}\).
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Notes
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This is a version of the issue pointed out by [4, p.119], that any inference-based description of an argument allows multiple arguments to be described in the same way. In fact what we have here is a stronger version of the problem, because [4] pointed out the problem for arguments which, in our terms, were described just by their grounds and conclusion. What we have here is the problem arising even when we state the inference rules as well. This issue the is converse of the problem that describing arguments by their entire structure, as \(\textsc {aspic}^{\mathsf {+}}\) and the assumption-based argumentation of [4] do, allows for redundant elements in the arguments, as we have just shown.
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Acknowledgements
This work was partially funded by EPSRC EP/P010105/1 Collaborative Mobile Decision Support for Managing Multiple Morbidities.
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Li, Z., Cohen, A., Parsons, S. (2018). Two Forms of Minimality in ASPIC\(^+\). In: Belardinelli, F., Argente, E. (eds) Multi-Agent Systems and Agreement Technologies. EUMAS AT 2017 2017. Lecture Notes in Computer Science(), vol 10767. Springer, Cham. https://doi.org/10.1007/978-3-030-01713-2_15
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