Common Knowledge Always, Forever

• URL: http://arxiv.org/abs/2602.13914v1
• Date: Sat, 14 Feb 2026 22:34:27 GMT
• Title: Common Knowledge Always, Forever
• Authors: Martín Diéguez, David Fernández-Duque,
• Abstract summary: We introduce a polytopological PDL capable of expressing common knowledge and various generalizations.<n>We show it has the finite model property over closure spaces but not over Cantor derivative spaces.
• Score: 3.4806267677524896
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: There has been an increasing interest in topological semantics for epistemic logic, which has been shown to be useful for, e.g., modelling evidence, degrees of belief, and self-reference. We introduce a polytopological PDL capable of expressing common knowledge and various generalizations and show it has the finite model property over closure spaces but not over Cantor derivative spaces. The latter is shown by embedding a version of linear temporal logic with `past', which does not have the finite model property.

Related papers

• Foundations of Diffusion Models in General State Spaces: A Self-Contained Introduction [54.95522167029998]
  This article is a self-contained primer on diffusion over general state spaces.<n>We develop the discrete-time view (forward noising via Markov kernels and learned reverse dynamics) alongside its continuous-time limits.<n>A common variational treatment yields the ELBO that underpins standard training losses.
  arXiv  Detail & Related papers  (2025-12-04T18:55:36Z)
• Dirac - von Neumann axioms in the setting of Continuous Model Theory [0.0]
  We recast the well-known axiom system of quantum mechanics used by physicists (the Dirac calculus) in the language of Continuous Logic.<n>For the basic version of the axiomatic system we prove that along with the canonical continuous model the axioms have approximate finite models of large sizes.
  arXiv  Detail & Related papers  (2025-10-30T19:15:18Z)
• Explainable Chain-of-Thought Reasoning: An Empirical Analysis on State-Aware Reasoning Dynamics [69.00587226225232]
  We introduce a state-aware transition framework that abstracts CoT trajectories into structured latent dynamics.<n>To characterize the global structure of reasoning, we model their progression as a Markov chain.<n>This abstraction supports a range of analyses, including semantic role identification, temporal pattern visualization, and consistency evaluation.
  arXiv  Detail & Related papers  (2025-08-29T18:53:31Z)
• A Survey on Latent Reasoning [100.54120559169735]
  Large Language Models (LLMs) have demonstrated impressive reasoning capabilities.<n>CoT reasoning that verbalizes intermediate steps limits the model's expressive bandwidth.<n>Latent reasoning tackles this bottleneck by performing multi-step inference entirely in the model's continuous hidden state.
  arXiv  Detail & Related papers  (2025-07-08T17:29:07Z)
• The Origins of Representation Manifolds in Large Language Models [52.68554895844062]
  We show that cosine similarity in representation space may encode the intrinsic geometry of a feature through shortest, on-manifold paths.<n>The critical assumptions and predictions of the theory are validated on text embeddings and token activations of large language models.
  arXiv  Detail & Related papers  (2025-05-23T13:31:22Z)
• Deep Learning is Not So Mysterious or Different [54.5330466151362]
  We argue that anomalous generalization behaviour is not distinct to neural networks.<n>We present soft inductive biases as a key unifying principle in explaining these phenomena.<n>We also highlight how deep learning is relatively distinct in other ways, such as its ability for representation learning.
  arXiv  Detail & Related papers  (2025-03-03T22:56:04Z)
• 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)
• Dual Box Embeddings for the Description Logic EL++ [16.70961576041243]
  Similar to Knowledge Graphs (KGs), Knowledge Graphs are often incomplete, and maintaining and constructing them has proved challenging. Similar to KGs, a promising approach is to learn embeddings in a latent vector space, while additionally ensuring they adhere to the semantics of the underlying DL. We propose a novel ontology embedding method named Box$2$EL for the DL EL++, which represents both concepts and roles as boxes.
  arXiv  Detail & Related papers  (2023-01-26T14:13:37Z)
• Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICA [4.340954888479091]
  We introduce a new general identifiable framework for principled disentanglement referred to as Structured Independent Component Analysis (SNICA) Our contribution is to extend the identifiability theory of deep generative models for a very broad class of structured models. We establish the major result that identifiability for this framework holds even in the presence of noise of unknown distribution.
  arXiv  Detail & Related papers  (2021-06-17T15:56:57Z)
• Plausible Reasoning about EL-Ontologies using Concept Interpolation [27.314325986689752]
  We propose an inductive mechanism which is based on a clear model-theoretic semantics, and can thus be tightly integrated with standard deductive reasoning. We focus on inference, a powerful commonsense reasoning mechanism which is closely related to cognitive models of category-based induction.
  arXiv  Detail & Related papers  (2020-06-25T14:19:41Z)
• 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.