Related papers: The matrices of argumentation frameworks
The visualization of argumentation frameworks (AFs) is crucial for enabling a wide applicability of argumentative tools. However, their visualization is often considered only as an accompanying part of tools for computing semantics and…
We propose a diagrammatic notation for matrix differentiation. Our new notation enables us to derive formulas for matrix differentiation more easily than the usual matrix (or index) notation. We demonstrate the effectiveness of our notation…
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is…
I compare the matrix representation of the basic statements of Special Relativity with the conventional vector space representation. It is shown, that the matrix form reproduces all equations in a very concise and elegant form, namely:…
We present a general formal argumentation system for dealing with the detachment of conditional obligations. Given a set of facts, constraints, and conditional obligations, we answer the question whether an unconditional obligation is…
In this paper, we address the problem of change in an abstract argumentation system. We focus on a particular change: the addition of a new argument which interacts with previous arguments. We study the impact of such an addition on the…
Abstract Dialectical Frameworks (ADFs) generalize Dung's argumentation frameworks allowing various relationships among arguments to be expressed in a systematic way. We further generalize ADFs so as to accommodate arbitrary acceptance…
Justification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification:…
Gradual argumentation frameworks represent arguments and their relationships in a weighted graph. Their graphical structure and intuitive semantics makes them a potentially interesting tool for interpretable machine learning. It has been…
In formal argumentation, a distinction can be made between extension-based semantics, where sets of arguments are either (jointly) accepted or not, and ranking-based semantics, where grades of acceptability are assigned to arguments.…
We present an extension-based approach for computing and verifying preferences in an abstract argumentation system. Although numerous argumentation semantics have been developed previously for identifying acceptable sets of arguments from…
In the present paper, the existence and multiplicity problems of extensions are addressed. The focus is on extension of the stable type. The main result of the paper is an elegant characterization of the existence and multiplicity of…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation…
The study of arguments as abstract entities and their interaction as introduced by Dung (Artificial Intelligence 177, 1995) has become one of the most active research branches within Artificial Intelligence and Reasoning. A main issue for…
This note reviews Section 2 of Dung's seminal 1995 paper on abstract argumentation theory. In particular, we clarify and make explicit all of the proofs mentioned therein, and provide more examples to illustrate the definitions, with the…
We present a new distributed representation in deep neural nets wherein the information is represented in native form as a matrix. This differs from current neural architectures that rely on vector representations. We consider matrices as…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
Underlying the theory of inferences, a primary task of logic is language analysis. Such a task can be understood as depending on a general theory of representation, taking as a starting point the idea that some entities (`` representations…
In abstract argumentation, multiple argumentation semantics have been proposed that allow to select sets of jointly acceptable arguments from a given argumentation framework, i.e. based only on the attack relation between arguments. The…