A QBF-based Formalization of Abstract Argumentation Semantics

Supported by the National Research Fund, Luxembourg (LAAMI project) and by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant ref. EP/J012084/1 (SAsSY project).Peer reviewedPostprin

Counting Complexity for Reasoning in Abstract Argumentation

In this paper, we consider counting and projected model counting of extensions in abstract argumentation for various semantics. When asking for projected counts we are interested in counting the number of extensions of a given argumentation framework while multiple extensions that are identical when restricted to the projected arguments count as only one projected extension. We establish classical complexity results and parameterized complexity results when the problems are parameterized by treewidth of the undirected argumentation graph. To obtain upper bounds for counting projected extensions, we introduce novel algorithms that exploit small treewidth of the undirected argumentation graph of the input instance by dynamic programming (DP). Our algorithms run in time double or triple exponential in the treewidth depending on the considered semantics. Finally, we take the exponential time hypothesis (ETH) into account and establish lower bounds of bounded treewidth algorithms for counting extensions and projected extension.Comment: Extended version of a paper published at AAAI-1

Argument-based Belief in Topological Structures

This paper combines two studies: a topological semantics for epistemic notions and abstract argumentation theory. In our combined setting, we use a topological semantics to represent the structure of an agent's collection of evidence, and we use argumentation theory to single out the relevant sets of evidence through which a notion of beliefs grounded on arguments is defined. We discuss the formal properties of this newly defined notion, providing also a formal language with a matching modality together with a sound and complete axiom system for it. Despite the fact that our agent can combine her evidence in a 'rational' way (captured via the topological structure), argument-based beliefs are not closed under conjunction. This illustrates the difference between an agent's reasoning abilities (i.e. the way she is able to combine her available evidence) and the closure properties of her beliefs. We use this point to argue for why the failure of closure under conjunction of belief should not bear the burden of the failure of rationality.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Civil Procedure as a Critical Discussion

This Article develops a model for analyzing legal dispute resolution systems as systems for argumentation. Our model meshes two theories of argument conceived centuries apart: contemporary argumentation theory and classical stasis theory. In this Article, we apply the model to the Federal Rules of Civil Procedure as a proof of concept. Specifically, the model analyzes how the Federal Rules of Civil Procedure function as a staged argumentative critical discussion designed to permit judge and jury to rationally resolve litigants’ differences in a reasonable manner. At a high level, this critical discussion has three phases: a confrontation, an (extended) opening, and a concluding phase. Those phases are the umbrella under which discrete argumentation phases occur at points we call stases. Whenever litigants seek a ruling or judgment, they reach a stasis—a stopping or standing point for arguing procedural points of disagreement. During these stases, the parties make arguments that fall into predictable “commonplace” argument types. Taken together, these stock argument types form a taxonomy of arguments for all civil cases. Our claim that the Federal Rules of Civil Procedure function as a system for argumentation is novel, as is our claim that civil cases breed a taxonomy of argument types. These claims also mark the beginning of a broader project. Starting here with the Federal Rules of Civil Procedure, we embark on a journey that we expect to follow for several years (and which we hope other scholars will join), exploring our model’s application across dispute resolution systems and using it to make normative claims about those systems. From a birds-eye view, this Article also represents a short modern trek in a much longer journey begun by advocates in city states in and near Greece nearly 2500 years ago