Discretisation for odd quadratic twists

The discretisation problem for even quadratic twists is almost understood, with the main question now being how the arithmetic Delaunay heuristic interacts with the analytic random matrix theory prediction. The situation for odd quadratic twists is much more mysterious, as the height of a point enters the picture, which does not necessarily take integral values (as does the order of the Shafarevich-Tate group). We discuss a couple of models and present data on this question.Comment: To appear in the Proceedings of the INI Workshop on Random Matrix Theory and Elliptic Curve

Argument Revision

Understanding the dynamics of argumentation systems is a crucial component in the de-velopment of computational models of argument that are used as representations of belief. To that end, in this paper, we introduce a model of Argument Revision, presented in terms of the contraction and revision of a system of structured argumentation. Argument Revi-sion is influenced by the AGM model of belief revision, but with certain key differences. Firstly, Argument Revision involves modifying the underlying model (system of argumen-tation) from which beliefs are derived, allowing for a finer-grained approach to modifying beliefs. Secondly, the richer structure provided by a system of argumentation permits a determination of minimal change based on quantifiable effects on the system as opposed to qualitative criteria such as entrenchment orderings. Argument Revision does, however, retain a close link to the AGM approach to belief revision. A basic set of postulates for rational revisions and contractions in Argument Revision is proposed; these postulates are influenced by, and capture the spirit of, those found in AGM belief revision. After specifying a determination of minimal change, based on measurable effects on the system, we conclude the paper by going on to show how Argument Revision can be used as a strategic tool by a participant in a multi-agent dialogue, assisting with commitment retraction and dishonesty. In systems of argumentation that contain even small knowledge bases, it is difficult for a dialogue participant to fully assess the impact of seemingly trivial changes to that knowledge base, or other parts of the system; we demonstrate, by means of an example, that Argument Revision solves this problem through a determination of minimal change that is justifiable and intuitive

A System for Dispute Mediation:The Mediation Dialogue Game

We propose a dialogue game for mediation and its formalization in DGDL. This dialectical system is available as software through Arvina for automatic execution. This work expands the literature in dialectical systems, in particular those for more than two players, and shows the practical impact on mediation activity through the opportunity offered to mediators once implemented

Debating Technology for Dialogical Argument:Sensemaking, Engagement and Analytics

Debating technologies, a newly emerging strand of research into computational technologies to support human debating, offer a powerful way of providing naturalistic, dialogue-based interaction with complex information spaces. The full potential of debating technologies for dialogical argument can, however, only be realized once key technical and engineering challenges are overcome, namely data structure, data availability, and interoperability between components. Our aim in this article is to show that the Argument Web, a vision for integrated, reusable, semantically rich resources connecting views, opinions, arguments, and debates online, offers a solution to these challenges. Through the use of a running example taken from the domain of citizen dialogue, we demonstrate for the first time that different Argument Web components focusing on sensemaking, engagement, and analytics can work in concert as a suite of debating technologies for rich, complex, dialogical argument

On the role of dialogue models in the age of large language models.

We argue that Machine learning, in particular the currently prevalent generation of Large Language Models (LLMs), can work constructively with existing normative models of dialogue as exemplified by dialogue games, specifically their computational applications within, for example, inter-agent communication and automated dialogue management. Furthermore we argue that this relationship is bi-directional, that some uses of dialogue games benefit from increased functionality due to the specific capabilities of LLMs, whilst LLMs benefit from externalised models of, variously, problematic, normative, or idealised behaviour. Machine Learning (ML) approaches, especially LLMs , appear to be making great advances against long-standing Artificial Intelligence challenges. In particular, LLMs are increasingly achieving successes in areas both adjacent to, and overlapping with, those of interest to the Computational Models of Natural Argument community. A prevalent opinion, not without some basis, within the ML research community is that many, if not all, AI challenges, will eventually be solved by ML models of increasing power and utility, negating the need for alternative or traditional approaches. An exemplar of this position, is the study of distinct models of dialogue for inter-agent communication when LLM based chatbots are increasingly able to surpass their performance in specific contexts. The trajectory of increased LLM capabilities suggests no reason that this trend will not continue, at least for some time. However, it is not the case that only the one, or the other approach, is necessary. Despite a tendency for LLMs to feature creep, and to appear to subsume additional areas of study, there are very good reasons to consider three modes of study of dialogue. Firstly, LLMs as their own individual field within ML, secondly, dialogue both in terms of actual human behaviour, which can exhibit wide quality standards, but also in terms of normative and idealised models, and thirdly, the fertile area in which the two overlap and can operate collaboratively. It is this third aspect with which this paper is concerned, for the first will occur anyway as researchers seek to map out the boundaries of what LLMs, as AI models, can actually achieve, and the second will continue, because the study of how people interact naturally through argument and dialogue will remain both fascinating and of objective value regardless of advances made in LLMs. However, where LLMs, Dialogue Models, and, for completion, people, come together, there is fertile ground for the development of principled models of interaction that are well-founded, well-regulated, and supportive of mixed-initiative interactions between humans and intelligent software agents

Reconsidering RepStat rules in dialectic games.

Prohibition of repeated statements has benefits for the tractability and predictability of dialogues carried out by machines, but doesn't match the real world behaviour of people. This gap between human and machine behaviour leads to problems when formal dialectical systems are applied in conversational AI contexts. However, the problem of handling statement repetition gives insight into wider issues that stem partly from the historical focus on formal dialectics to the near exclusion of descriptive dialectics. In this paper we consider the problem of balancing the needs of machines versus those of human participants through the consideration of both descriptive and formal dialectics integrated within a single overarching dialectical system. We describe how this approach can be supported through minimal extension of the Dialogue Game Description Language

Towards a declarative approach to constructing dialogue games.

In this paper we sketch a new approach to the development of dialogue games that builds upon the knowledge gained from several decades of dialogue game research across a variety of communities and which leverages the capabilities of the Dialogue Game Description Language as a means to describe the constituent parts of dialogue games. Our ultimate aim is to produce a method for rapidly describing and implementing games that conform to the designer's needs by declaring what is required and then automatically constructing the game from components, called 'fragments', that are distilled from existing dialogue games

Integrating argumentation with social conversation between multiple virtual coaches

This paper presents progress and challenges in developing a platform for multi-character, argumentation based, interaction with a group of virtual coaches for healthcare advice and promotion of healthy behaviours. Several challenges arise in the development of such a platform, e. g., choosing the most effective way of utilising argumentation between the coaches with multiple perspectives, handling the presentation of these perspectives and finally, the personalisation and adaptation of the platform to the user types. In this paper, we present the three main challenges recognized, and show how we aim to address these.</p

A dialogue game for multi-party goal-setting in health coaching

Goal-setting is a frequently adopted strategy in behaviour change coaching. When setting a goal, it is important that it is understood and agreed upon by all parties, and not simply accepted as-is. We present here a dialogue game for multi-party goal-setting, in which multiple health coaches can contribute in order to find a goal that is acceptable to both the patient, and the coaches themselves. Our proposed game incorporates three important aspects of goal-setting and health coaching, (1) coaches can query each other's proposed goals, (2) the patient takes ownership of the goal, and (3) the patient themselves can propose goals