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[2602.13914] Common Knowledge Always, Forever
Summary
The paper discusses a polytopological PDL framework for expressing common knowledge and its implications in epistemic logic, highlighting its finite model property.
Why It Matters
This research contributes to the field of epistemic logic by introducing a new framework that enhances understanding of common knowledge, which is crucial for various applications in artificial intelligence and logic. The findings regarding the finite model property have implications for how knowledge is modeled in computational contexts.
Key Takeaways
- Introduces a polytopological PDL framework for common knowledge.
- Demonstrates the finite model property over closure spaces.
- Highlights limitations over Cantor derivative spaces.
- Connects common knowledge with temporal logic concepts.
- Provides insights for applications in AI and epistemic reasoning.
Computer Science > Logic in Computer Science arXiv:2602.13914 (cs) [Submitted on 14 Feb 2026] Title:Common Knowledge Always, Forever Authors:Martín Diéguez, David Fernández-Duque View a PDF of the paper titled Common Knowledge Always, Forever, by Mart\'in Di\'eguez and David Fern\'andez-Duque View PDF HTML (experimental) 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. Comments: Subjects: Logic in Computer Science (cs.LO); Artificial Intelligence (cs.AI) Cite as: arXiv:2602.13914 [cs.LO] (or arXiv:2602.13914v1 [cs.LO] for this version) https://doi.org/10.48550/arXiv.2602.13914 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Journal reference: Festschrift for Andreas Herzig on the Occasion of his 65th Birthday. Essays in Honor of Andi, 2026 Submission history From: Martin Dieguez [view email] [v1] Sat, 14 Feb 2026 22:34:27 UTC (32 KB) Full-text links: Access Paper: View a PDF of the paper titled Common Knowledge Always, Forever, by Mart\'in Di\'eguez and David Fern\'andez-Duq...