Title Abstract Contents 1 2 3 4 5 Acknowlegments References Footnotes


[1] For some recent discussions of structured arguments, the reader is referred to e.g. the work of Pollock (1994), Vreeswijk (1993), or Verheij (1995a, 1995b).

[2] Our argumentation theories correspond to Dung's argumentation frameworks. Our defeaters are his attacks.

[3] Dung's definitions of complete and grounded extensions are left out.

[4] Even stronger, unions of admissible sets with non-empty intersection are admissible, as Dung shows. This follows from two observations: (i) If Args is a subset of Args', then any Args-acceptable argument Arg is Args'-acceptable. (ii) If Args is admissible and Arg is Args-acceptable, then Args v {Arg} is conflict-free.

[5] In this paper the definitions of Verheij (1995a, 1995b) are restricted in two ways. First, there the influence of the structure of arguments on argumentation is considered, in particular in cases of accrual of reasons and sequential weakening. Second, Verheij (1995b) argues that defeat can be compound, meaning that the status of arguments depends on relations of groups of arguments. In this paper, and in Dung's (1995), only single arguments can challenge other single arguments.

[6] Our complete stage extensions have no relation with Dung's complete extensions (cf. note [3]).

[7] Verheij (1995a, 1995b) defines which defeaters are relevant for a stage with range Range. The relevant defeaters are exactly the defeaters in Defeaters|Range.

[8] Verheij (1995a, 1995b) gives similar diagrams.

[9] On the right, only the canonical admissible stages (and their twins) are shown. The directions of the arrows do not correspond to taking a particular argument into account, as in the previous diagrams.

[10] As a result, stages (UndefeatedArgs1, DefeatedArgs1) and (UndefeatedArgs2, DefeatedArgs2) are compatible if and only if (UndefeatedArgs1 v UndefeatedArgs2, DefeatedArgs1 v DefeatedArgs2) is a stage.

Title Abstract Contents 1 2 3 4 5 Acknowlegments References Footnotes