Abstract
A common assumption for argumentation-based dialogues is that any argument exchanged is complete, in the sense that its premises entail its claim. However, in real world dialogues, agents commonly exchange enthymemes—arguments with incomplete logical structure. This paper formalises the dialogical exchange of enthymemes that are missing some constituent elements, such that it is not possible to directly entail the claim of the intended argument from the premises of the enthymeme exchanged. This can lead to misunderstandings between agents; we provide a rich set of locutions for identifying and resolving such misunderstandings, and a protocol that governs the use of these. We show that, under certain conditions, the status of moves made during a dialogue conforming to our system corresponds with the status of arguments in the Dung argument framework instantiated by the contents of the moves made at that stage in the dialogue. This is significant since it ensures that the use of enthyememes does not prevent the agents from reaching the appropriate decision according to the information they have shared.
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Notes
- 1.
Notice that before \(Ag_1\) seeks clarification, although it appears that \(Ag_2\) wins the dialogue (since she moves \(E_2\) against A), \(E_2\) does not formally attack A (since \(E_2\) does not negate any element of A) and so \(Ag_1\)’s argument A is determined acceptable according to the AF constructed by the contents of the enthymemes revealed by the agents. In other words, a mismatch can exist between the pragmatic and the logical conclusions implied by a dialogue in which enthymemes are used.
- 2.
[4] formalises a dialogical generalisation of \(\textit{ASPIC}^{+}\) extended to accommodate reasoning about preferences; however soundness and completeness results are not shown.
- 3.
Note that in this paper we do not utilise the \(\textit{ASPIC}^{+}\) distinction between the disjoint sets of axiom (\(K_n\)) and ordinary (\(K_p\)) premises (\(K=K_n \cup K_p\)), whereby only ordinary premises are fallible and so can be challenged/attacked.
- 4.
Recall, here we deal only with forward extension of enthymemes, so that an ‘upwards extendable enthymeme’ is an enthymeme that can potentially be forward extended.
- 5.
We assume that the participants of a dialogue have the same preferences and so they agree to whether an argument A defeats an argument B or not.
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Xydis, A., Hampson, C., Modgil, S., Black, E. (2021). Towards a Sound and Complete Dialogue System for Handling Enthymemes. In: Baroni, P., Benzmüller, C., Wáng, Y.N. (eds) Logic and Argumentation. CLAR 2021. Lecture Notes in Computer Science(), vol 13040. Springer, Cham. https://doi.org/10.1007/978-3-030-89391-0_24
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