Abstract argumentation and answer set programming: two faces of Nelson's logic

• URL: http://arxiv.org/abs/2203.14405v1
• Date: Sun, 27 Mar 2022 22:18:44 GMT
• Title: Abstract argumentation and answer set programming: two faces of Nelson's logic
• Authors: Jorge Fandinno and Luis Fari\~nas del Cerro
• Abstract summary: We show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson's constructive logic N4. We do so by formalizing, in this logic, two principles that we call non-contradictory inference and strengthened closed world assumption.
• Score: 7.513733974830771
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson's constructive logic N4. We do so by formalizing, in this logic, two principles that we call non-contradictory inference and strengthened closed world assumption: the first states that no belief can be held based on contradictory evidence while the latter forces both unknown and contradictory evidence to be regarded as false. Using these principles, both logic programming and abstract argumentation frameworks are translated into constructive logic in a modular way and using the object language. Logic programming implication and abstract argumentation supports become, in the translation, a new implication connective following the non-contradictory inference principle. Attacks are then represented by combining this new implication with strong negation. Under consideration in Theory and Practice of Logic Programming (TPLP).

Related papers

• Towards Generalizable and Faithful Logic Reasoning over Natural Language via Resolution Refutation [24.584926992534346]
  We propose a novel framework, named Generalizable and Faithful Reasoner (GFaiR), which introduces the paradigm of resolution refutation. Resolution refutation has the capability to solve all first-order logic reasoning problems by extending reasoning rules and employing the principle of proof by contradiction. Our system outperforms previous works by achieving state-of-the-art performances in complex scenarios while maintaining performances in simple scenarios.
  arXiv  Detail & Related papers  (2024-04-02T06:28:44Z)
• Chain of Logic: Rule-Based Reasoning with Large Language Models [10.017812995997753]
  Rule-based reasoning enables us to draw conclusions by accurately applying a rule to a set of facts. We introduce a new prompting method, Chain of Logic, which elicits rule-based reasoning through decomposition and recomposition. We evaluate chain of logic across eight rule-based reasoning tasks involving three distinct compositional rules from the LegalBench benchmark.
  arXiv  Detail & Related papers  (2024-02-16T01:54:43Z)
• Language Models can be Logical Solvers [99.40649402395725]
  We introduce LoGiPT, a novel language model that directly emulates the reasoning processes of logical solvers. LoGiPT is fine-tuned on a newly constructed instruction-tuning dataset derived from revealing and refining the invisible reasoning process of deductive solvers.
  arXiv  Detail & Related papers  (2023-11-10T16:23:50Z)
• Modeling Hierarchical Reasoning Chains by Linking Discourse Units and Key Phrases for Reading Comprehension [80.99865844249106]
  We propose a holistic graph network (HGN) which deals with context at both discourse level and word level, as the basis for logical reasoning. Specifically, node-level and type-level relations, which can be interpreted as bridges in the reasoning process, are modeled by a hierarchical interaction mechanism.
  arXiv  Detail & Related papers  (2023-06-21T07:34:27Z)
• Argumentative Characterizations of (Extended) Disjunctive Logic Programs [2.055949720959582]
  We show that assumption-based argumentation can represent not only normal logic programs, but also disjunctive logic programs and their extensions. We consider some inference rules for disjunction that the core logic of the argumentation frameworks should respect.
  arXiv  Detail & Related papers  (2023-06-12T14:01:38Z)
• MetaLogic: Logical Reasoning Explanations with Fine-Grained Structure [129.8481568648651]
  We propose a benchmark to investigate models' logical reasoning capabilities in complex real-life scenarios. Based on the multi-hop chain of reasoning, the explanation form includes three main components. We evaluate the current best models' performance on this new explanation form.
  arXiv  Detail & Related papers  (2022-10-22T16:01:13Z)
• Discourse-Aware Graph Networks for Textual Logical Reasoning [142.0097357999134]
  Passage-level logical relations represent entailment or contradiction between propositional units (e.g., a concluding sentence) We propose logic structural-constraint modeling to solve the logical reasoning QA and introduce discourse-aware graph networks (DAGNs) The networks first construct logic graphs leveraging in-line discourse connectives and generic logic theories, then learn logic representations by end-to-end evolving the logic relations with an edge-reasoning mechanism and updating the graph features.
  arXiv  Detail & Related papers  (2022-07-04T14:38:49Z)
• A natural deduction system for orthomodular logic [0.0]
  Orthomodular logic is a weakening of quantum logic in the sense of Birkhoff and von Neumann. It is shown to be a nonlinear noncommutative logic. It is extended to two systems of predicate logic: the first is sound for Takeuti's quantum set theory, and the second is sound for a variant of Weaver's quantum logic.
  arXiv  Detail & Related papers  (2021-09-11T22:28:17Z)
• Abstract Reasoning via Logic-guided Generation [65.92805601327649]
  Abstract reasoning, i.e., inferring complicated patterns from given observations, is a central building block of artificial general intelligence. This paper aims to design a framework for the latter approach and bridge the gap between artificial and human intelligence. We propose logic-guided generation (LoGe), a novel generative DNN framework that reduces abstract reasoning as an optimization problem in propositional logic.
  arXiv  Detail & Related papers  (2021-07-22T07:28:24Z)
• Higher-order Logic as Lingua Franca -- Integrating Argumentative Discourse and Deep Logical Analysis [0.0]
  We present an approach towards the deep, pluralistic logical analysis of argumentative discourse. We use state-of-the-art automated reasoning technology for classical higher-order logic.
  arXiv  Detail & Related papers  (2020-07-02T11:07:53Z)
• Logical Neural Networks [51.46602187496816]
  We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning) Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation. Inference is omni rather than focused on predefined target variables, and corresponds to logical reasoning.
  arXiv  Detail & Related papers  (2020-06-23T16:55:45Z)

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.