Cyclic Supports in Recursive Bipolar Argumentation Frameworks: Semantics and LP Mapping

• URL: http://arxiv.org/abs/2408.08916v1
• Date: Wed, 14 Aug 2024 16:06:16 GMT
• Title: Cyclic Supports in Recursive Bipolar Argumentation Frameworks: Semantics and LP Mapping
• Authors: Gianvincenzo Alfano, Sergio Greco, Francesco Parisi, Irina Trubitsyna,
• Abstract summary: We present classical semantics for the Bipolar Argumentation Framework (BAF) and the Recursive BAF (Rec-BAF) This is achieved by providing a modular definition of the sets of defeated and acceptable elements for each BAF-based framework. We also characterize, in an elegant and uniform way, the semantics of general BAF and Rec-BAF in terms of logic programming and partial stable model semantics.
• Score: 19.799266797193344
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Dung's Abstract Argumentation Framework (AF) has emerged as a key formalism for argumentation in Artificial Intelligence. It has been extended in several directions, including the possibility to express supports, leading to the development of the Bipolar Argumentation Framework (BAF), and recursive attacks and supports, resulting in the Recursive BAF (Rec-BAF). Different interpretations of supports have been proposed, whereas for Rec-BAF (where the target of attacks and supports may also be attacks and supports) even different semantics for attacks have been defined. However, the semantics of these frameworks have either not been defined in the presence of support cycles, or are often quite intricate in terms of the involved definitions. We encompass this limitation and present classical semantics for general BAF and Rec-BAF and show that the semantics for specific BAF and Rec-BAF frameworks can be defined by very simple and intuitive modifications of that defined for the case of AF. This is achieved by providing a modular definition of the sets of defeated and acceptable elements for each AF-based framework. We also characterize, in an elegant and uniform way, the semantics of general BAF and Rec-BAF in terms of logic programming and partial stable model semantics.

Related papers

• An Encoding of Abstract Dialectical Frameworks into Higher-Order Logic [57.24311218570012]
  This approach allows for the computer-assisted analysis of abstract dialectical frameworks. Exemplary applications include the formal analysis and verification of meta-theoretical properties.
  arXiv  Detail & Related papers  (2023-12-08T09:32:26Z)
• A Semantic Approach to Decidability in Epistemic Planning (Extended Version) [72.77805489645604]
  We use a novel semantic approach to achieve decidability. Specifically, we augment the logic of knowledge S5$_n$ and with an interaction axiom called (knowledge) commutativity. We prove that our framework admits a finitary non-fixpoint characterization of common knowledge, which is of independent interest.
  arXiv  Detail & Related papers  (2023-07-28T11:26:26Z)
• DELPHIC: Practical DEL Planning via Possibilities (Extended Version) [76.75197961194182]
  This work aims to push the envelop of practical DEL planning. We propose an equivalent semantics defined using, as main building block, so-called possibilities. To substantiate this claim, we implement both approaches in ASP and we set up an experimental evaluation to compare DELPHIC with the traditional, Kripke-based approach.
  arXiv  Detail & Related papers  (2023-07-28T10:09:45Z)
• Non-flat ABA is an Instance of Bipolar Argumentation [23.655909692988637]
  Assumption-based Argumentation (ABA) is a well-known structured argumentation formalism. A common restriction imposed on ABA frameworks (ABAFs) is that they are flat. No translation exists from general, possibly non-flat ABAFs into any kind of abstract argumentation formalism.
  arXiv  Detail & Related papers  (2023-05-21T13:18:08Z)
• Guiding the PLMs with Semantic Anchors as Intermediate Supervision: Towards Interpretable Semantic Parsing [57.11806632758607]
  We propose to incorporate the current pretrained language models with a hierarchical decoder network. By taking the first-principle structures as the semantic anchors, we propose two novel intermediate supervision tasks. We conduct intensive experiments on several semantic parsing benchmarks and demonstrate that our approach can consistently outperform the baselines.
  arXiv  Detail & Related papers  (2022-10-04T07:27:29Z)
• Admissibility in Strength-based Argumentation: Complexity and Algorithms (Extended Version with Proofs) [1.5828697880068698]
  We study the adaptation of admissibility-based semantics to Strength-based Argumentation Frameworks (StrAFs) Especially, we show that the strong admissibility defined in the literature does not satisfy a desirable property, namely Dung's fundamental lemma. We propose a translation in pseudo-Boolean constraints for computing (strong and weak) extensions.
  arXiv  Detail & Related papers  (2022-07-05T18:42:04Z)
• 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)
• Towards Robustness Against Natural Language Word Substitutions [87.56898475512703]
  Robustness against word substitutions has a well-defined and widely acceptable form, using semantically similar words as substitutions. Previous defense methods capture word substitutions in vector space by using either $l$-ball or hyper-rectangle.
  arXiv  Detail & Related papers  (2021-07-28T17:55:08Z)
• On graded semantics of abstract argumentation: Extension-based case [0.0]
  This paper considers some issues on extension-based semantics for abstract argumentation framework (AAF) An alternative fundamental lemma is given, which generalizes the corresponding result obtained in [1]. A number of fundamental semantics for AAF, including conflict-free, admissible, complete and stable semantics, are shown to be closed under reduced meet modulo an ultrafilter.
  arXiv  Detail & Related papers  (2020-12-19T04:32:19Z)
• 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)
• Expressiveness of SETAFs and Support-Free ADFs under 3-valued Semantics [15.174903837196297]
  We shed light on the relation between SETAFs and support-free ADFs. It is only the presence of unsatisfiable acceptance conditions in support-free ADFs that discriminate the two approaches.
  arXiv  Detail & Related papers  (2020-07-07T16:03:23Z)

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.