Abstract Dialectical Frameworks: Advanced Tools for Formal Argumentation

Argumentation is an area at the intersection of Philosophy, Artificial Intelligence (AI) and several application domains. Within AI, formal models of arguments and their relationships, as well as the necessary conflict resolution in the presence of diverging opinions are studied. One prototypical model of argumentation is the instantiation-based approach which is performed in three steps: (i) generation of arguments and conflicts from a given knowledge base; (ii) conflict evaluation by abstracting away from the arguments` contents yielding sets of collectively accepted arguments; (iii) drawing conclusions from accepted arguments in terms of the initial knowledge base. For Step (ii), Dung`s argumentation frameworks are the most frequently used tools, not the least due to their elegance and simplicity. However, this simplicity comes with several shortcomings in the abstraction step. In particular, auxiliary arguments are required to model situations where arguments are collectively in conflict with another one or conflicts are conditional. In this project, we aim at overcoming these problems but retain the general idea underlying the abstract, instantiation based approach to argumentation. To this end, we want to advance the research of a novel formalism for abstract argumentation, namely abstract dialectical frameworks (ADFs), recently proposed by the principal investigators of this project. ADFs are able to act as an intermediate layer in the instantiation process solving the aforementioned problems with Dung`s frameworks. The fundamental idea of ADFs is to treat arguments as atomic entities, yet to allow for much more flexible relationships among arguments by specifying these relations as logical formulae. The project goals can be listed along four axes: first, we need to further develop the theory of ADFs. Second, we want to focus on the dynamics of argumentation exploiting the fact that the logic-based specification in ADFs allows to directly apply methods from disciplines such as belief change and diagnosis. Third, we have to analyse the full potential of ADFs in the instantiation-based argumentation process. Finally, we will provide implementations and systems for ADFs, paving the way towards argumentation tools for practical application scenarios.

Argumentation is an area at the intersection of Philosophy, Artificial Intelligence (AI) and several application domains. Within AI, formal models of arguments and their relationships, as well as the necessary conflict resolution in the presence of diverging opinions are studied. A prototypical model of argumentation is the instantiation-based approach which is typically performed in three steps:First, the generation of arguments and conflicts from a given knowledge base is performed; second, conflict evaluation by abstracting away from the arguments' contents yields sets of collectively accepted arguments; third, one draws conclusions from accepted arguments in terms of the initial knowledge base. For the second step, Dung's argumentation frameworks are the most frequently used tools, not the least due to their elegance and simplicity. However, this simplicity comes with several shortcomings in the abstraction step. In this project, we tackled these problems but retained the general idea underlying the abstract, instantiation based approach to argumentation. To this end, we advanced the research of a novel formalism for abstract argumentation, namely abstract dialectical frameworks (ADFs), proposed by the principal investigators of this project. ADFs are able to act as an intermediate layer in the instantiation process solving the aforementioned problems with Dung's frameworks. The fundamental idea of ADFs is to treat arguments as atomic entities, yet to allow for much more flexible relationships among arguments by specifying these relations as logical formulae.The results in the project are manifold: first we had to revise some of the basic semantics, later in the project further novel semantics for ADFs were proposed and the computational complexity of reasoning in ADFs has been analyzed in detail. The concept of dynamics of ADFs required more fundamental research than expected, but led to a series of important contributions, also for Dung's argumentation frameworks. We also investigated the role of ADFs in the instantiation-based process.As an example, it has been shown how defeasible reasoning scenarios based on rules with exceptions can be captured via an instantiation of ADFs. Prototypical systems for ADFs have been implemented (using ASP and QBF technology) and system-related methods like splitting have been studied.Finally, extensions of the formalism have been proposed during the project, e.g. an approach to take probabilities into account. One of the major outcomes in this context, however, is our initial work on GRAPPA (GRaph-based Argument Processing with Patterns of Acceptance). Rather than specifying acceptance conditions in a logic, GRAPPA takes the popularity of graphical models in argumentation (and AI in general) seriously. Instead of specifying acceptance conditions in terms of propositional or some other logic, GRAPPA allows acceptance conditions to be specified in terms of the labels of links in an argumentation graph. A successor project on this new graph-based formalism has recently been granted as a bilateral joint project (DFG BR 1817/7-2; FWF I2854).