In memoriam Douglas N. Walton: the influence of Doug Walton on AI and law

Doug Walton, who died in January 2020, was a prolific author whose work in informal logic and argumentation had a profound influence on Artificial Intelligence, including Artificial Intelligence and Law. He was also very interested in interdisciplinary work, and a frequent and generous collaborator. In this paper seven leading researchers in AI and Law, all past programme chairs of the International Conference on AI and Law who have worked with him, describe his influence on their work

Burden of Persuasion in Argumentation

This paper provides a formal model for the burden of persuasion in dialogues, and in particular, in legal proceedings. The model shows how an allocation of the burden of persuasion may induce single outcomes in dialectical contexts in which, without such an allocation, the status of conflicting arguments would remain undecided. Our approach is based on a two-stage labelling. The first-stage labelling determines what arguments are accepted, rejected or undecided, regardless of the allocation of burden. The second-stage labelling revises the dialectical status of first-stage undecided arguments, according to burdens of persuasion. The labelling is finally extended in such a way as to obtain a complete labelling. Our model combines two ideas that have emerged in the debate on the burden of persuasion: the idea that the burden of persuasion determines the solution of conflicts between arguments, and the idea that its satisfaction depends on the dialectical status of the arguments concerned. Our approach also addresses inversions of the burden of persuasion, namely, cases in which the burden of persuasion over an argument does not extend to its subarguments.Comment: In Proceedings ICLP 2020, arXiv:2009.0915

Weakly-admissible Semantics and the Propagation of Ambiguity in Abstract Argumentation Semantics

The concept of ambiguous literals of defeasible logics is mapped to the set of undecided arguments identified by an argumentation semantics. It follows that Dung’s complete semantics are all ambiguity propagating, since the undecided status of an attacking argument is always propagated to the attacked argument, unless the latter is defeated by another accepted argument. In this paper we investigate a novel family of abstract argumentation semantics, called weakly-admissible semantics, where we do not require an acceptable argument to be necessarily defended from the attacks of undecided arguments. Weakly-admissible semantics are conflict-free, ambiguity blocking, non-admissible (in Dung’s sense), but employing a more relaxed defence-based notion of admissibility; they allow reinstatement and generate extensions that are super-sets of grounded semantics, and they at least accept credulously what Dung’s complete semantics accept at least credulously

How to formalize informal logic

This paper presents a formalization of informal logic using the Carneades Argumentation System, a formal, computational model of argument that consists of a formal model of argument graphs and audiences. Conflicts between pro and con arguments are resolved using proof standards, such as preponderance of the evidence. Carneades also formalizes argumentation schemes. Schemes can be used to check whether a given argument instantiates the types of argument deemed normatively appropriate for the type of dialogue

A Proposal to Embed the In Dubio Pro Reo Principle into Abstract Argumentation Semantics based on Topological Ordering and Undecidedness Propagation

Abstract. In this paper we discuss how the in dubio pro reo principle and the corresponding standard of proof beyond reasonable doubt can be modelled in abstract argumentation. The in dubio pro reo principle protects arguments against attacks from doubtful arguments. We identify doubtful arguments with a subset of undecided arguments, called active undecided arguments, consisting of cyclic arguments responsible for generating the undecided situation. We obtain the standard of proof beyond reasonable doubt by imposing that attacks from doubtful undecided arguments are not enough to change the acceptability status of an attacked argument (the reo). The resulting semantics, called SCCvoid semantics, are defined using a SCC-recursive schema. The semantics are conflict-free, non-admissible (in Dung’s sense), but employing a more relaxed defence-based notion of admissibility; they allow reinstatement and they accept credulously what the corresponding complete semantics accepts at least credulously

Beyond reasonable doubt: a proposal for undecidedness blocking in abstract argumentation

In Dung’s abstract semantics, the label undecided is always propagated from the attacker to the attacked argument, unless the latter is also attacked by an accepted argument. In this work we propose undecidedness blocking abstract argumentation semantics where the undecided label is confined to the strong connected component where it was generated and it is not propagated to the other parts of the argumentation graph. We show how undecidedness blocking is a fundamental reasoning pattern absent in abstract argumentation but present in similar fashion in the ambiguity blocking semantics of Defeasible logic, in the beyond reasonable doubt legal principle or when someone gives someone else the benefit of the doubt. The resulting semantics, called SCC-void semantics, are defined using an SCC-recursive schema. The semantics are conflict-free and non-admissible, but they incorporate a more relaxed defence-based notion of admissibility. They allow reinstatement and they credulously accept what the corresponding Dung’s complete semantics accepts at least credulously

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

Arguing about causes in law: a semi-formal framework for causal arguments

In legal argumentation and liability attribution, disputes over causes play a central role. Legal discussions about causation often have difficulty with cause-in-fact in complex situations, e.g. overdetermination, preemption, omission. We first assess three theories of causation. Then we introduce a semi-formal framework to model causal arguments using both strict and defeasible rules. We apply the framework to the Althen vaccine injury case. Wrapping up the paper, we motivate a causal argumentation framework and propose to integrate current theories of causation