Extending Belief Change to Advance Dynamics in Argumentation

Within Artificial Intelligence (AI), a key field that studies foundations of how to revise or update given knowledge in a formalized form is belief change. The area of belief change provides general-purpose approaches to investigate properties that are desirable, or considered rational, when revising or updating one`s knowledge or beliefs. In AI, a domain with strong inherent need for handling dynamically evolving knowledge is argumentation. Generally speaking, argumentation in AI studies how arguments are represented, and conflicts among them can be resolved, by specifying criteria of acceptable or unacceptable arguments. Argumentation is, naturally, a dynamic process, where arguments and counterarguments may be posed in an evolving debate. Argumentation can come in many forms, and, accordingly, many formalizations formal models of arguments and their relations have been developed to fit the diverse needs of argumentation. Recent research on dynamics of argumentation has, mainly, focused on a specific, and simple yet fundamental formal model, which is, in a sense, a common core to many other formal models. Nevertheless, the formal models in this field form a very heterogeneous picture, and many miss proper handling of dynamics. To avoid ad-hoc approaches for each formal model, and the resulting fragmentation, we aim to apply the general-purpose tools provided by belief change, which can support a principled approach to develop dynamic methods for argumentation. However, operations studied in belief change do not cover all of the core dynamic operations in argumentation, and thus also the general-purpose tools cannot cover argumentation in its generality. This is the motivation and starting point of our proposed project. We aim to extend current methods in belief change to allow for a principled approach that covers dynamics in argumentation and enables development of novel dynamic methods for the diverse formal models. In addition to benefit argumentation, our project will also increase the reach of methods of belief change. This project will address both theoretical and practical aspects. In addition to providing a general framework, we will develop new dynamic methods, and investigate these in detail. We aim to study theoretical properties of the new methods, such as complexity, which gives an impression on how hard it is to compute the result of these methods, as well as address practical issues by designing and implementing concrete systems.

This research project investigated foundational research questions in the field of computational argumentation, which is situated in the wider field of Artificial Intelligence (AI). Argumentation in AI has several aims, among them the goal to study how to formally represent arguments, how to draw conclusions based on such arguments, and how one can relate arguments. Formal approaches to representation of arguments are a useful endeavour, since they allow for formal specifications leading to automated reasoning procedures. In our project we studied modifications to argument structures or sets of such argument structures. We viewed such modifications in a general sense, e.g., including selecting a minimal number of arguments from a set to be prepared to defend goals in a debate, revising or aggregating multiple arguments, and abstracting argument structure to simplify an argumentation scenario. The scientific contribution of the project can be roughly divided into two directions. Firstly, we considered certain desiderata on operations that modify given argument structures. Such desiderata can be used, e.g., to specify general properties modifications should have. Secondly, we investigated the computational complexity of change operators, which is a basis for subsequent algorithm design and implementations. Inspired by the established field of belief change, we showed possibility and impossibility results regarding desiderata. That is, we showed that in some cases there exist operations satisfying desiderata, while for others there is no operator that satisfies all of them, e.g., because two desiderata are incompatible. Based on these insights, we showed that systematic adaptation of desiderata can lead to situations where again change operators exist. We studied complexity of several change operations. Under the term complexity we mean here a classification of problems (or questions) according to the efficiency of solving them. We showed that the variety of change operations is also reflected in a variety of complexity classes, that is, different change operations also differ greatly in their computational complexity. Such results form a basis for algorithm design, e.g., by choosing adequate algorithmic tools for a problem of certain complexity. Without sophisticated algorithm design it is unlikely to find an efficient algorithm for a complex problem. We provided prototypical implementations for our algorithms that oftentimes constitute the current state of the art in efficient solving of certain problems. Summarizing, this research project enabled finding deeper insights into computational argumentation. However, also novel challenges and questions arose during the course of the project. For instance, it became clear that preferential approaches to arguments, which, e.g., reflect different views on strengths of arguments, lead to a significantly more complex picture, and more research is needed on this topic. Likewise, tools that support explanations based on argumentative reasoning are in need of further research.