CARBON a Web application and a RESTful API for argumentation

This thesis documents the development of Collaborative Argumentation Brought Online (CARBON). Collaborative Argumentation Brought Online (CARBON) aims to make abstract dialectical frameworks (ADFs) available via HTTP by providing a RESTful API and a JavaScript heavy application, that allows to use ADFs in a wiki context on top of that API. The thesis summarizes basic concepts of abstract argumentation using examples of Dung argumentation frameworks (AFs), bipolar argumentation frameworks (BAFs) and abstract dialectical frameworks (ADFs). The advantages of using Haskell as a programming language for server side software are demonstrated by discussing central concepts of functional programming and how these influenced the design or our solutions and simplified the creation of a RESTful API. It is described, how argumentation can be embedded in a wiki, and how a mapping between wiki articles and statements can be established to enable users to create new content while still being able to work with ADFs. To simplify the creation of acceptance conditions, a custom approach to proof standards is presented that allows to translate a bipolar argumentation framework (BAF) with proof standards into a ADF

A framework for relating, implementing and verifying argumentation models and their translations

Computational argumentation theory deals with the formalisation of argument structure, conflict between arguments and domain-specific constructs, such as proof standards, epistemic probabilities or argument schemes. However, despite these practical components, there is a lack of implementations and implementation methods available for most structured models of argumentation and translations between them. This thesis addresses this problem, by constructing a general framework for relating, implementing and formally verifying argumentation models and translations between them, drawing from dependent type theory and the Curry-Howard correspondence. The framework provides mathematical tools and programming methodologies to implement argumentation models, allowing programmers and argumentation theorists to construct implementations that are closely related to the mathematical definitions. It furthermore provides tools that, without much effort on the programmer's side, can automatically construct counter-examples to desired properties, while finally providing methodologies that can prove formal correctness of the implementation in a theorem prover. The thesis consists of various use cases that demonstrate the general approach of the framework. The Carneades argumentation model, Dung's abstract argumentation frameworks and a translation between them, are implemented in the functional programming language Haskell. Implementations of formal properties of the translation are provided together with a formalisation of AFs in the theorem prover, Agda. The result is a verified pipeline, from the structured model Carneades into existing efficient SAT-based implementations of Dung's AFs. Finally, the ASPIC+ model for argumentation is generalised to incorporate content orderings, weight propagation and argument accrual. The framework is applied to provide a translation from this new model into Dung's AFs, together with a complete implementation

Formal Methods of Argumentation as Models of Engineering Design Decisions and Processes

Complex engineering projects comprise many individual design decisions. As these decisions are made over the course of months, even years, and across different teams of engineers, it is common for them to be based on different, possibly conflicting assumptions. The longer these inconsistencies go undetected, the costlier they are to resolve. Therefore it is important to spot them as early as possible. There is currently no software aimed explicitly at detecting inconsistencies in interrelated design decisions. This thesis is a step towards the development of such tools. We use formal methods of argumentation, a branch of artificial intelligence, as the foundation of a logical model of design decisions capable of handling inconsistency. It has three parts. First, argumentation is used to model the pros and cons of individual decisions and to reason about the possible worlds in which these arguments are justified. In the second part we study sequences of interrelated decisions. We identify cases where the arguments in one decision invalidate the justification for another decision, and develop a measure of the impact that choosing a specific option has on the consistency of the overall design. The final part of the thesis is concerned with non-deductive arguments, which are used in design debates, for example to draw analogies between past and current problems. Our model integrates deductive and non-deductive arguments side-by-side. This work is supported by our collaboration with the engineering department of Queen’s University Belfast and an industrial partner. The thesis contains two case studies of realistic problems and parts of it were implemented as software prototypes. We also give theoretical results demonstrating the internal consistency of our model

A framework for relating, implementing and verifying argumentation models and their translations

Computational argumentation theory deals with the formalisation of argument structure, conflict between arguments and domain-specific constructs, such as proof standards, epistemic probabilities or argument schemes. However, despite these practical components, there is a lack of implementations and implementation methods available for most structured models of argumentation and translations between them. This thesis addresses this problem, by constructing a general framework for relating, implementing and formally verifying argumentation models and translations between them, drawing from dependent type theory and the Curry-Howard correspondence. The framework provides mathematical tools and programming methodologies to implement argumentation models, allowing programmers and argumentation theorists to construct implementations that are closely related to the mathematical definitions. It furthermore provides tools that, without much effort on the programmer's side, can automatically construct counter-examples to desired properties, while finally providing methodologies that can prove formal correctness of the implementation in a theorem prover. The thesis consists of various use cases that demonstrate the general approach of the framework. The Carneades argumentation model, Dung's abstract argumentation frameworks and a translation between them, are implemented in the functional programming language Haskell. Implementations of formal properties of the translation are provided together with a formalisation of AFs in the theorem prover, Agda. The result is a verified pipeline, from the structured model Carneades into existing efficient SAT-based implementations of Dung's AFs. Finally, the ASPIC+ model for argumentation is generalised to incorporate content orderings, weight propagation and argument accrual. The framework is applied to provide a translation from this new model into Dung's AFs, together with a complete implementation

Tools for the implementation of argumentation models

The structured approach to argumentation has seen a surge of models, introducing a multitude of ways to deal with the formalisation of arguments. However, while the development of the mathematical models have flourished, the actual implementations and development of methods for implementation of these models have been lagging behind. This paper attempts to alleviate this problem by providing methods that simplify implementation, i.e. we demonstrate how the functional programming language Haskell can naturally express mathematical definitions and sketch how a theorem prover can verify this implementation. Furthermore, we provide methods to streamline the documenting of code, showing how literate programming allows the implementer to write formal definition, implementation and documentation in one file. All code has been made publicly available and reusable