Notes on neighborhood semantics for logics of unknown truths and false beliefs

• URL: http://arxiv.org/abs/2002.09622v1
• Date: Sat, 22 Feb 2020 04:27:04 GMT
• Title: Notes on neighborhood semantics for logics of unknown truths and false beliefs
• Authors: Jie Fan
• Abstract summary: We study logics of unknown truths and false beliefs under neighborhood semantics. It turns out that they are incomparable over various classes of neighborhood models. We extend the results to the case of public announcements.
• Score: 1.827510863075184
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this article, we study logics of unknown truths and false beliefs under neighborhood semantics. We compare the relative expressivity of the two logics. It turns out that they are incomparable over various classes of neighborhood models, and the combination of the two logics are equally expressive as standard modal logic over any class of neighborhood models. We propose morphisms for each logic, which can help us explore the frame definability problem, show a general soundness and completeness result, and generalize some results in the literature. We axiomatize the two logics over various classes of neighborhood frames. Last but not least, we extend the results to the case of public announcements, which has good applications to Moore sentences and some others.

Related papers

• Toward Conceptual Modeling for Propositional Logic: Propositions as Events [0.0]
  This paper reflects on applying propositional logic language to a high-level diagrammatic representation called the thinging machines (TM) model. The ultimate research objective is a quest for a thorough semantic alignment of TM modeling and propositional logic into a single structure.
  arXiv  Detail & Related papers  (2024-09-24T03:45:24Z)
• Disentangling Logic: The Role of Context in Large Language Model Reasoning Capabilities [31.728976421529577]
  We investigate the contrast across abstract and contextualized logical problems from a comprehensive set of domains. We focus on standard propositional logic, specifically propositional deductive and abductive logic reasoning. Our experiments aim to provide insights into disentangling context in logical reasoning and the true reasoning capabilities of LLMs.
  arXiv  Detail & Related papers  (2024-06-04T21:25:06Z)
• LogicBench: Towards Systematic Evaluation of Logical Reasoning Ability of Large Language Models [52.03659714625452]
  Recently developed large language models (LLMs) have been shown to perform remarkably well on a wide range of language understanding tasks. But, can they really "reason" over the natural language? This question has been receiving significant research attention and many reasoning skills such as commonsense, numerical, and qualitative have been studied.
  arXiv  Detail & Related papers  (2024-04-23T21:08:49Z)
• LOGICSEG: Parsing Visual Semantics with Neural Logic Learning and Reasoning [73.98142349171552]
  LOGICSEG is a holistic visual semantic that integrates neural inductive learning and logic reasoning with both rich data and symbolic knowledge. During fuzzy logic-based continuous relaxation, logical formulae are grounded onto data and neural computational graphs, hence enabling logic-induced network training. These designs together make LOGICSEG a general and compact neural-logic machine that is readily integrated into existing segmentation models.
  arXiv  Detail & Related papers  (2023-09-24T05:43:19Z)
• The Transformation Logics [58.35574640378678]
  We introduce a new family of temporal logics designed to balance the trade-off between expressivity and complexity. Key feature is the possibility of defining operators of a new kind that we call transformation operators. We show them to yield logics capable of creating hierarchies of increasing expressivity and complexity.
  arXiv  Detail & Related papers  (2023-04-19T13:24:04Z)
• Morpho-logic from a Topos Perspective: Application to symbolic AI [2.781492199939609]
  Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI) We propose to further develop and generalize this link between mathematical morphology and modal logic from a topos perspective. We show that the modal logic is well adapted to define concrete and efficient operators for revision, merging, and abduction of new knowledge, or even spatial reasoning.
  arXiv  Detail & Related papers  (2023-03-08T21:24:25Z)
• 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)
• Abstract argumentation and answer set programming: two faces of Nelson's logic [7.513733974830771]
  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.
  arXiv  Detail & Related papers  (2022-03-27T22:18:44Z)
• Foundations of Reasoning with Uncertainty via Real-valued Logics [70.43924776071616]
  We give a sound and strongly complete axiomatization that can be parametrized to cover essentially every real-valued logic. Our class of sentences are very rich, and each describes a set of possible real values for a collection of formulas of the real-valued logic.
  arXiv  Detail & Related papers  (2020-08-06T02:13:11Z)
• 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.