  Abstract Dialectical Frameworks (ADFs) generalize Dung's argumentation
frameworks allowing various relationships among arguments to be expressed in a
systematic way. We further generalize ADFs so as to accommodate arbitrary
acceptance degrees for the arguments. This makes ADFs applicable in domains
where both the initial status of arguments and their relationship are only
insufficiently specified by Boolean functions. We define all standard ADF
semantics for the weighted case, including grounded, preferred and stable
semantics. We illustrate our approach using acceptance degrees from the unit
interval and show how other valuation structures can be integrated. In each
case it is sufficient to specify how the generalized acceptance conditions are
represented by formulas, and to specify the information ordering underlying the
characteristic ADF operator. We also present complexity results for problems
related to weighted ADFs.
