A game-theoretic perspective on the notion of argument strength in abstract argumentation

This paper is concerned with the problem of quantifying the strength of arguments in controversial debates, which we model as abstract argumentation frameworks [Dung, 1995]. Standard approaches to abstract argumentation provide only a qualitative account of the status of arguments, whereas numerical measures of argument strength might provide a more precise evaluation of their individual status. Intuitively, the strength of an argument in a debate essentially depends on how a proponent of that argument would defend himself against the criticisms of someone opposed to the argument. Since there can be many ways of defending and attacking an opinion, we essentially conceive argument strength as an equilibrium resulting from the interactions taking place between the opinions that a proponent and an opponent of the argument could a priori embrace. More formally, we define argument strength in terms of the value of a repeated two-person zero-sum strategic game with imperfect information. Then, using the game-theoretic properties of such games and notably the von Neumann minimax theorem [Neumann, 1928], we establish and illustrate the main properties of this new argument strength measure

The Algebra of Open and Interconnected Systems

Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes, automata, Petri nets, chemical reaction networks, and so on. The key feature is that the language is comprised of a number of components with multiple (input/output) terminals, each possibly labelled with some type, that may then be connected together along these terminals to form a larger network. The components form hyperedges between labelled vertices, and so a diagram in this language forms a hypergraph. We formalise the compositional structure by introducing the notion of a hypergraph category. Network-style diagrammatic languages and their semantics thus form hypergraph categories, and semantic interpretation gives a hypergraph functor. The first part of this thesis develops the theory of hypergraph categories. In particular, we introduce the tools of decorated cospans and corelations. Decorated cospans allow straightforward construction of hypergraph categories from diagrammatic languages: the inputs, outputs, and their composition are modelled by the cospans, while the 'decorations' specify the components themselves. Not all hypergraph categories can be constructed, however, through decorated cospans. Decorated corelations are a more powerful version that permits construction of all hypergraph categories and hypergraph functors. These are often useful for constructing the semantic categories of diagrammatic languages and functors from diagrams to the semantics. To illustrate these principles, the second part of this thesis details applications to linear time-invariant dynamical systems and passive linear networks.Comment: 230 pages. University of Oxford DPhil Thesi

A Systematic Approach to Constructing Incremental Topology Control Algorithms Using Graph Transformation

Communication networks form the backbone of our society. Topology control algorithms optimize the topology of such communication networks. Due to the importance of communication networks, a topology control algorithm should guarantee certain required consistency properties (e.g., connectivity of the topology), while achieving desired optimization properties (e.g., a bounded number of neighbors). Real-world topologies are dynamic (e.g., because nodes join, leave, or move within the network), which requires topology control algorithms to operate in an incremental way, i.e., based on the recently introduced modifications of a topology. Visual programming and specification languages are a proven means for specifying the structure as well as consistency and optimization properties of topologies. In this paper, we present a novel methodology, based on a visual graph transformation and graph constraint language, for developing incremental topology control algorithms that are guaranteed to fulfill a set of specified consistency and optimization constraints. More specifically, we model the possible modifications of a topology control algorithm and the environment using graph transformation rules, and we describe consistency and optimization properties using graph constraints. On this basis, we apply and extend a well-known constructive approach to derive refined graph transformation rules that preserve these graph constraints. We apply our methodology to re-engineer an established topology control algorithm, kTC, and evaluate it in a network simulation study to show the practical applicability of our approachComment: This document corresponds to the accepted manuscript of the referenced journal articl

Design and Politics: Metadesign for social change

In recent years, a collaborative approach to solving socio-urban problems has become common. In some cases, organizational changes have been worked out in enterprises and governments to accommodate the collaborative process, and people started recognizing the already present collaborative aspect of the creative process. Nevertheless, a rigorous theoretical/conceptual background that can sustain continuous social innovation based on accountable experimentation is still majorly lacking in these contexts. The specific approach elaborated for Metadesign by the author can provide a bridge between these innovative intentions and a new epistemological framework that has emerged from contemporary philosophy, anthropology, and complexity theory. In the context of the so-called “Smart City”, Metadesign could serve as an accessible approach to the democratic organization of communities so they can perform qualified and consequential creative work, including rethinking their own role in urban planning (meta-action). This approach is based on a new social interaction repertoire, partially derived from the popularization of digital interaction, but also from a new epistemic: complexity theory involves extreme shifts in the prevailing epistemological outlook, requiring new cognitive tools to cope with the increasing cognitive load in social interaction needed in collaborative creative work. This new epistemic also involves changing the way we frame objects of knowledge, recognizing new “objects of design”, of particular interest to the Metadesign action, that can mediate social change in a concerted and conscious manner.Keywords: metadesign, urban planning, social change, innovation, micro-politics, smart cities