Abstract
This paper presents a formal model of dialectical argument strength in terms of the number of ways in which an argument can be successfully attacked in expansions of an abstract argumentation framework. First a model is proposed that is abstract but designed to avoid overly limiting assumptions on instantiations or dialogue contexts. It is then shown that most principles for argument strength proposed in the literature fail to hold for the proposed notions of dialectical strength, which clarifies the rational foundations of these principles and highlights the importance of distinguishing between kinds of argument strength, in particular logical, dialectical and rhetorical argument strength. The abstract model is then instantiated with ASPIC+ to test the claim that it does not make overly limiting assumptions on the structure of arguments and the nature of their relations.
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