We provide an overview of the current state of the art in formal argumentation theory. The focus is on how the how to use argumentation theory for inferring what to believe or what to do, given a potentially conflicting knowledge base of strict and defeasible inference rules. We examine how to construct arguments from such a knowledge base, how to determine which argument attacks which other argument, and how to determine which conclusions (inferences) can be considered as overall justified. A well-engineered argumentation formalism should make sure that a set of justified conclusions satisfies some reasonable properties, so we examine what these properties are and how they can be satisfied. We also study how argument-based inference can be expressed in terms of structured discussion.

The tutorial will contain a number of short questions and exercises, and the audience is encouraged to bring pen and paper with them. We will round off with a list of concrete open research issues, of which some proper solutions are being sought.

The tutorial aims to explain the following topics:

- the notion of an argument scheme, and how these can be encoded by strict and defeasible rules
- the notion of an argumentation framework, and how these can be generated from an underlying knowledge base
- the concepts of admissibility and strong admissibility, in both their extensions and labellings form
- the concept of argumentation semantics, in both its extensions form and labellings form; we will focus on complete, grounded, preferred, stable, semi-stable and ideal semantics
- the notion of rationality postulates; how to make sure that an argumentation formalism produces an outcome that can be regarded as reasonable
- the different approaches for satisfying the rationality postulates, as well as their advantages and disadvantages
- an overview of discussion-based interpretations of argumentation semantics; how do the different semantics of argumentation frameworks relate to the ability to win a particular type of discussion?
- an overview of some concrete open research issues in the area of formal argumentation and non-monotonic reasoning

We want to point out that the current tutorial will *not* discuss
the topic of argumentation implementations and solvers, as these would merit a
separate tutorial.

The target audience is composed of three main groups. The first group consists of PhD students and early career researchers working in the field of logic and AI, nonmonotonic reasoning and argumentation theory. The second group consists of established scholars in fields like natural language processing, text mining and deep learning who would be interested in using techniques from formal argumentation theory in their work. The third group consists of established scholars in argumentation theory whose expertise is mainly in abstract argumentation theory and who would like to understand the research issues in instantiated argumentation, where the aim is to logically infer what to do or what to believe.

The only required prerequisite knowledge is some basic understanding of propositional logic notation and inference.

Cardiff University

School of Computer Science and Informatics

Queen's Buildings

5 The Parade

Cardiff CF24 2LQ

Wales, United Kingdom

email: CaminadaM@cardiff.ac.uk

phone: +44 29 2087 0109

Martin Caminada is one of the prominent scholars in the field of computational argumentation. His work has been published at venues such as IJCAI, ECAI, AAAI, AAMAS, AIJ and JAIR. Some of the results of his work (such as argument labellings, semi-stable semantics and rationality postulates) are now used by other researchers as the basis of their work. He has an h-index of 27 (source: Google Scholar), has authored and co-authored four different handbook chapters, and has given tutorials at ESSLLI and EASSS, as well as at IJCAI 2009.

A full list of publications is available at https://users.cs.cf.ac.uk/CaminadaM/publications.html

The tutorial is based upon the following three chapters in the Handbook of Formal Argumentation:

- P. Baroni, M.W.A. Caminada and M. Giacomin.
Abstract Argumentation Frameworks and their Semantics

(the emphasis will be on sections 1-3.8, 3.11 and 4.1) - M.W.A. Caminada. Rationality Postulates: applying argumentation theory for non-monotonic reasoning
- M.W.A. Caminada. Argumentation Semantics as Formal Discussion

The tutorial slides are available both in LibreOffice and PDF format.

A related tutorial on the connection between argumentation and machine learning will be given by Federico Cerutti.