Related papers: The matrices of argumentation frameworks
Argument graphs provide an abstract representation of an argumentative situation. A bipolar argument graph is a directed graph where each node denotes an argument, and each arc denotes the influence of one argument on another. Here we…
We propose a novel ranking-based semantics for Dung-style argumentation frameworks with the help of conditional logics. Using an intuitive translation for an argumentation framework to generate conditionals, we can apply nonmonotonic…
It is a mystery which input features contribute to a neural network's output. Various explanation (feature attribution) methods are proposed in the literature to shed light on the problem. One peculiar observation is that these explanations…
The recent Control Argumentation Framework (CAF) is a generalization of Dung's Argumentation Framework which handles argumentation dynamics under uncertainty; especially it can be used to model the behavior of an agent which can anticipate…
An abstract argumentation framework can be used to model the argumentative stance of an agent at a high level of abstraction, by indicating for every pair of arguments that is being considered in a debate whether the first attacks the…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
Deep learning has become the dominant approach for creating high capacity, scalable models across diverse data modalities. However, because these models rely on a large number of learned parameters, tightly couple feature extraction with…
In this article, we present a novel approach for parsing argumentation structures. We identify argument components using sequence labeling at the token level and apply a new joint model for detecting argumentation structures. The proposed…
Abstract argumentation frameworks (AFs) provide a formal setting to analyze many forms of reasoning with conflicting information. While the expressiveness of general infinite AFs make them a tempting tool for modeling many kinds of…
Argumentation theory is a powerful paradigm that formalizes a type of commonsense reasoning that aims to simulate the human ability to resolve a specific problem in an intelligent manner. A classical argumentation process takes into account…
Dung's abstract argumentation frameworks model acceptability solely in terms of an attack relation, thereby conflating two conceptually distinct aspects of argumentative reasoning: direct conflict between arguments and the structural…
Directed mixed graphs permit directed and bidirected edges between any two vertices. They were first considered in the path analysis developed by Sewall Wright and play an essential role in statistical modeling. We introduce a matrix…
In dialogical argumentation it is often assumed that the involved parties always correctly identify the intended statements posited by each other, realize all of the associated relations, conform to the three acceptability states (accepted,…
The connection between inconsistent databases and Dung's abstract argumentation framework has recently drawn growing interest. Specifically, an inconsistent database, involving certain types of integrity constraints such as functional and…
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Determinantal formulas, relation to conformal field models and the theory of Generalized Kontsevich model are discussed in some…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
In the context of abstract argumentation, we present the benefits of considering temporality, i.e. the order in which arguments are enunciated, as well as causality. We propose a formal method to rewrite the concepts of acyclic abstract…
We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and…
In this paper, we propose a fresh perspective on argumentation semantics, to view them as a relational database. It offers encapsulation of the underlying argumentation graph, and allows us to understand argumentation semantics under a…
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…