Abstract Interpretation in Formal Argumentation: with a Galois Connection for Abstract Dialectical Frameworks and May-Must Argumentation (First Report)

• URL: http://arxiv.org/abs/2007.12474v1
• Date: Wed, 22 Jul 2020 04:26:15 GMT
• Title: Abstract Interpretation in Formal Argumentation: with a Galois Connection for Abstract Dialectical Frameworks and May-Must Argumentation (First Report)
• Authors: Ryuta Arisaka and Takayuki Ito
• Abstract summary: Labelling-based formal argumentation relies on labelling functions that typically assign one of 3 labels to indicate either acceptance, rejection, or else undecided-to-be-either. Abstract dialectical frameworks (ADF) is a well-known argumentation formalism that belongs to this category. We prove that there is a Galois connection between MMA and ADF, in which is a concretisation of MMA and MMA is an abstraction of ADF.
• Score: 3.7311680121118336
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Labelling-based formal argumentation relies on labelling functions that typically assign one of 3 labels to indicate either acceptance, rejection, or else undecided-to-be-either, to each argument. While a classical labelling-based approach applies globally uniform conditions as to how an argument is to be labelled, they can be determined more locally per argument. Abstract dialectical frameworks (ADF) is a well-known argumentation formalism that belongs to this category, offering a greater labelling flexibility. As the size of an argumentation increases in the numbers of arguments and argument-to-argument relations, however, it becomes increasingly more costly to check whether a labelling function satisfies those local conditions or even whether the conditions are as per the intention of those who had specified them. Some compromise is thus required for reasoning about a larger argumentation. In this context, there is a more recently proposed formalism of may-must argumentation (MMA) that enforces still local but more abstract labelling conditions. We identify how they link to each other in this work. We prove that there is a Galois connection between them, in which ADF is a concretisation of MMA and MMA is an abstraction of ADF. We explore the consequence of abstract interpretation at play in formal argumentation, demonstrating a sound reasoning about the judgement of acceptability/rejectability in ADF from within MMA. As far as we are aware, there is seldom any work that incorporates abstract interpretation into formal argumentation in the literature, and, in the stated context, this work is the first to demonstrate its use and relevance.

Related papers

• Rejection in Abstract Argumentation: Harder Than Acceptance? [18.299322342860513]
  We consider flexible conditions for emphrejecting an argument from an extension, which we call rejection conditions (RCs) Rejection AFs are highly expressive, giving rise to natural problems on higher levels of the hierarchy.
  arXiv  Detail & Related papers  (2024-08-20T09:37:04Z)
• CASA: Causality-driven Argument Sufficiency Assessment [79.13496878681309]
  We propose CASA, a zero-shot causality-driven argument sufficiency assessment framework. PS measures how likely introducing the premise event would lead to the conclusion when both the premise and conclusion events are absent. Experiments on two logical fallacy detection datasets demonstrate that CASA accurately identifies insufficient arguments.
  arXiv  Detail & Related papers  (2024-01-10T16:21:18Z)
• A Unifying Framework for Learning Argumentation Semantics [50.69905074548764]
  We present a novel framework, which uses an Inductive Logic Programming approach to learn the acceptability semantics for several abstract and structured argumentation frameworks in an interpretable way. Our framework outperforms existing argumentation solvers, thus opening up new future research directions in the area of formal argumentation and human-machine dialogues.
  arXiv  Detail & Related papers  (2023-10-18T20:18:05Z)
• Semi-Abstract Value-Based Argumentation Framework [0.0]
  Phan Minh Dung proposed abstract argumentation framework, which models argumentation using directed graphs where structureless arguments are the nodes and attacks among the arguments are the edges. This thesis showcases two such extensions -- value-based argumentation framework by Trevor Bench-Capon (2002) and semi-abstract argumentation framework by Esther Anna Corsi and Christian Ferm" The contribution of this thesis is two-fold. Firstly, the new semi-abstract value-based argumentation framework is introduced. This framework maps propositional formulae associated with individual arguments to a set of ordered values.
  arXiv  Detail & Related papers  (2023-09-25T13:10:56Z)
• Ranking-based Argumentation Semantics Applied to Logical Argumentation (full version) [2.9005223064604078]
  We investigate the behaviour of ranking-based semantics for structured argumentation. We show that a wide class of ranking-based semantics gives rise to so-called culpability measures.
  arXiv  Detail & Related papers  (2023-07-31T15:44:33Z)
• Unsupervised Mapping of Arguments of Deverbal Nouns to Their Corresponding Verbal Labels [52.940886615390106]
  Deverbal nouns are verbs commonly used in written English texts to describe events or actions, as well as their arguments. The solutions that do exist for handling arguments of nominalized constructions are based on semantic annotation. We propose to adopt a more syntactic approach, which maps the arguments of deverbal nouns to the corresponding verbal construction.
  arXiv  Detail & Related papers  (2023-06-24T10:07:01Z)
• Semantic Role Labeling Meets Definition Modeling: Using Natural Language to Describe Predicate-Argument Structures [104.32063681736349]
  We present an approach to describe predicate-argument structures using natural language definitions instead of discrete labels. Our experiments and analyses on PropBank-style and FrameNet-style, dependency-based and span-based SRL also demonstrate that a flexible model with an interpretable output does not necessarily come at the expense of performance.
  arXiv  Detail & Related papers  (2022-12-02T11:19:16Z)
• A Formalisation of Abstract Argumentation in Higher-Order Logic [77.34726150561087]
  We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using interactive and automated reasoning tools.
  arXiv  Detail & Related papers  (2021-10-18T10:45:59Z)
• Strong Admissibility for Abstract Dialectical Frameworks [0.0]
  We present the concept of strong admissibility of interpretations for ADFs. We show that strongly admissible interpretations of ADFs form a lattice with the grounded interpretation as top element.
  arXiv  Detail & Related papers  (2020-12-10T21:50:35Z)
• Measuring Association Between Labels and Free-Text Rationales [60.58672852655487]
  In interpretable NLP, we require faithful rationales that reflect the model's decision-making process for an explained instance. We demonstrate that pipelines, existing models for faithful extractive rationalization on information-extraction style tasks, do not extend as reliably to "reasoning" tasks requiring free-text rationales. We turn to models that jointly predict and rationalize, a class of widely used high-performance models for free-text rationalization whose faithfulness is not yet established.
  arXiv  Detail & Related papers  (2020-10-24T03:40:56Z)
• Broadening Label-based Argumentation Semantics with May-Must Scales (May-Must Argumentation) [3.7311680121118336]
  Labeling-based approach allows for concise and flexible determination of acceptability statuses of arguments. We show that the broadened label-based semantics can be used to express more mild indeterminacy than inconsistency for acceptability judgement.
  arXiv  Detail & Related papers  (2020-01-16T10:24:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.