An abstract framework for formalising persuasion dialogues has recently been proposed. The framework provides for a range of speech acts, and protocols of varying levels of flexibility. However, the framework assumes the availability of preference information relevant to determining whether arguments moved in a dialogue defeat each other. However, preference information may only become available after the dialogue has terminated. Hence, in this paper, we describe dialogues conducted under the assumption of an attack relation that does not account for preferences. We then describe how the resultant dialogue graph can be pruned by a preference relation in order to determine whether the winner of the dialogue is still the winner given the newly available preference information. We also describe a class of protocols that account for subsequent pruning by a preference relation, and show that under a restriction on the pruning, if the player defending the dialogue's main topic is winning the dialogue, then (s)he remains the winner irrespective of the preference relation applied.
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