Forgetting an Argument

The notion of forgetting, as considered in the famous paper by Lin and Reiter in 1994 has been extensively studied in classical logic and more recently, in non-monotonic formalisms like logic programming. In this paper, we convey the idea of forgetting to another major AI formalism, namely Dungstyle argumentation frameworks. Our approach is axiomaticdriven and not limited to any specific semantics: we propose semantical and syntactical desiderata encoding different criteria for what forgetting an argument might mean; analyze how these criteria relate to each other; and check whether the criteria can be satisfied in general. The analysis is done for a number of widely used argumentation semantics. Our investigation shows that almost all desiderata are individually satis- fiable. However, combinations of semantical and/or syntactical conditions reveal a much more interesting landscape. For instance, we found that the ad hoc approach to forgetting an argument, i. e. , by the syntactical removal of the argument and all of its associated attacks, is too restrictive and only compatible with the two weakest semantical desiderata. Amongst the several interesting combinations identified, we showed that one satisfies a notion of minimal change and presented an algorithm that given an AF F and argument x, constructs a suitable AF G satisfying the conditions in the combination.

Authors

• Ringo Baumann
• Dov Gabbay
• Odinaldo Rodrigues

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