Three Kinds of Negation in Knowledge and Their Mathematical Foundations

• URL: http://arxiv.org/abs/2505.24422v1
• Date: Fri, 30 May 2025 10:01:37 GMT
• Title: Three Kinds of Negation in Knowledge and Their Mathematical Foundations
• Abstract summary: We examine and analyze the understanding and characteristics of negation in various fields such as philosophy, logic, and linguistics.<n>Based on the distinction between the concepts of contradiction and opposition, we propose that there are three different types of negation in knowledge from a conceptual perspective.
• Score: 4.343358400426713
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the field of artificial intelligence, understanding, distinguishing, expressing, and computing the negation in knowledge is a fundamental issue in knowledge processing and research. In this paper, we examine and analyze the understanding and characteristics of negation in various fields such as philosophy, logic, and linguistics etc. Based on the distinction between the concepts of contradiction and opposition, we propose that there are three different types of negation in knowledge from a conceptual perspective: contradictory negation, opposite negation, and intermediary negation. To establish a mathematical foundation that fully reflects the intrinsic connections, properties, and laws of these different forms of negation, we introduce SCOI: sets with contradictory negation, opposite negation and intermediary negation, and LCOI: logic with contradictory negation, opposite negation and intermediary negation, and we proved the main operational properties of SCOI as well as the formal inference relations in LCOI.

Related papers

• Three Types of Negation of Triple and its Elements and an Extension of Triple [0.6345523830122167]
  The TCOI triple is a semantic and structural extension of the classical triple.<n>This paper explores the expressive power and reasoning of the TCOI triple, as well as the application of TCOI triple implication reasoning in counterfactuals and counterfactual reasoning.
  arXiv  Detail & Related papers  (2026-09-08T05:26:43Z)
• Modus Tollens and Counterfactuals and Counterfactual Reasoning Based on Three Types of Negation [0.6345523830122167]
  We propose three variants of Modus Tollens corresponding to distinct negation types, namely MTC: Modus Tollens based on contradictory negation, MTO: Modus Tollens based on opposite negation, and MTI: Modus Tollens based on intermediary negation.<n>We show that the truth value algorithms for MTC, MTO and MTI can be as the truth value algorithms for the three counterfactuals reasoning based on different logical negations.
  arXiv  Detail & Related papers  (2026-09-07T13:38:23Z)
• Formal Concept Analysis with Three Types of Negation [0.6345523830122167]
  We introduce three types of negation concepts (contradictory negation, opposite negation, intermediary negation) into FCA.<n>Based on the set SCOI and logic LCOI+PLCOI, we define formal context, Galois connection operators, formal concept and concept lattice with three types of negation.<n>For the reasoning in FCACOI, this paper focuses on attribute implication reasoning. Based on the logic LCOI+PLCOI and its semantics, we introduce the notion of ICOI-entailment.
  arXiv  Detail & Related papers  (2026-08-29T14:54:04Z)
• How Language Models Process Negation [56.41361273288279]
  We study how Large Language Models (LLMs) process negation mechanistically.<n>Our work deepens the understanding of LLMs' internals, highlighting construction-dominant computations and the coexistence of competing mechanisms.
  arXiv  Detail & Related papers  (2026-05-04T18:17:05Z)
• Commonsense Knowledge with Negation: A Resource to Enhance Negation Understanding [17.1556206397938]
  Negation is a common and important semantic feature in natural language.<n>Large Language Models (LLMs) struggle when negation is involved in natural language understanding tasks.<n>We present a novel approach to automatically augment existing commonsense knowledge corpora with negation.
  arXiv  Detail & Related papers  (2026-04-21T19:00:28Z)
• Mastering Negation: Boosting Grounding Models via Grouped Opposition-Based Learning [87.15765427638195]
  We introduce D-Negation, a new dataset that provides objects annotated with both positive and negative semantic descriptions.<n>We propose a grouped opposition-based learning framework that learns negation-aware representations from limited samples.<n>By fine-tuning fewer than 10 percent of the model parameters, our approach achieves improvements of up to 4.4 mAP and 5.7 mAP on positive and negative semantic evaluations.
  arXiv  Detail & Related papers  (2026-03-13T03:21:48Z)
• Are Language Models Efficient Reasoners? A Perspective from Logic Programming [109.47572890883248]
  Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of human-like reasoning: efficiency.<n>We propose a framework for assessing LM reasoning efficiency through the lens of logic programming.
  arXiv  Detail & Related papers  (2025-10-29T15:30:31Z)
• Vision-Language Models Do Not Understand Negation [50.27667000027403]
  NegBench is a benchmark designed to evaluate negation understanding across 18 task variations and $79$k examples.<n>We show that this approach can result in a 10% increase in recall on negated queries and a 28% boost in accuracy on multiple-choice questions with negated captions.
  arXiv  Detail & Related papers  (2025-01-16T09:55:42Z)
• Paraphrasing in Affirmative Terms Improves Negation Understanding [9.818585902859363]
  Negation is a common linguistic phenomenon. We show improvements with CondaQA, a large corpus requiring reasoning with negation, and five natural language understanding tasks.
  arXiv  Detail & Related papers  (2024-06-11T17:30:03Z)
• Revisiting subword tokenization: A case study on affixal negation in large language models [57.75279238091522]
  We measure the impact of affixal negation on modern English large language models (LLMs) We conduct experiments using LLMs with different subword tokenization methods. We show that models can, on the whole, reliably recognize the meaning of affixal negation.
  arXiv  Detail & Related papers  (2024-04-03T03:14:27Z)
• Contrastive Learning for Inference in Dialogue [56.20733835058695]
  Inference, especially those derived from inductive processes, is a crucial component in our conversation. Recent large language models show remarkable advances in inference tasks. But their performance in inductive reasoning, where not all information is present in the context, is far behind deductive reasoning.
  arXiv  Detail & Related papers  (2023-10-19T04:49:36Z)
• Not another Negation Benchmark: The NaN-NLI Test Suite for Sub-clausal Negation [59.307534363825816]
  Negation is poorly captured by current language models, although the extent of this problem is not widely understood. We introduce a natural language inference (NLI) test suite to enable probing the capabilities of NLP methods.
  arXiv  Detail & Related papers  (2022-10-06T23:39:01Z)
• Improving negation detection with negation-focused pre-training [58.32362243122714]
  Negation is a common linguistic feature that is crucial in many language understanding tasks. Recent work has shown that state-of-the-art NLP models underperform on samples containing negation. We propose a new negation-focused pre-training strategy, involving targeted data augmentation and negation masking.
  arXiv  Detail & Related papers  (2022-05-09T02:41:11Z)
• Learning Disentangled Representations of Negation and Uncertainty [25.11863604063283]
  Linguistic theory postulates that expressions of negation and uncertainty are semantically independent from each other and the content they modify. We attempt to disentangle the representations of negation, uncertainty, and content using a Variational Autoencoder.
  arXiv  Detail & Related papers  (2022-04-01T15:12:05Z)
• Conversational Negation using Worldly Context in Compositional Distributional Semantics [0.0]
  Given a word, our framework can create its negation similar to how humans perceive negation. We propose and motivate a new logical negation using matrix inverse. We conclude that the combination of subtraction negation and phaser in the basis of the negated word yields the highest Pearson correlation of 0.635 with human ratings.
  arXiv  Detail & Related papers  (2021-05-12T16:04:36Z)
• Negation in Cognitive Reasoning [0.5801044612920815]
  Negation is an operation in formal logic and in natural language. One task of cognitive reasoning is answering questions given by sentences in natural language.
  arXiv  Detail & Related papers  (2020-12-23T13:22:53Z)
• Logic, Language, and Calculus [8.475081627511166]
  The difference between object-language and metalanguage is crucial for logical analysis, but has yet not been examined for the field of computer science. It is argued that inferential relations in a metalanguage (like a calculus for propositional logic) cannot represent conceptual relations of natural language.
  arXiv  Detail & Related papers  (2020-07-06T00:52:54Z)
• 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.